It is viable. Swim was playing a similar but more aggro oriented deck:

Riot has plans to release more Obliterate cards in the future, i would not worry too much about it.

I am a bit shocked that a "relatively new player" is bringing such a legit question to the table but getting so many poor answers from experienced users.

Simple Answer: Build a deck with 3 copies of Radiant Guardian. 

Deep Answer: With the exception of Lifesteal units, Heal cards are not cost-effective in this game.
There is a good reason why Burn aggro is the top S tier deck right now. 
Cards like Withering Wail can even do more harm then good due Crimson Disciple and Transfusion
Grasp of the Undying is another joke. Best target is Crimson Disciple, paying 3 extra mana to heal 3 is terrible. 
Vile Feast is decent, and just decent. Killing a Legion Grenadier to get a 1/1 token while taking 1 to the face is not exactly a great trade / counter play.
I just counted, burn aggro has a grand total of 48 direct damage to the nexus. Good luck enduring the early game just to lose the middle game. 

Sustained Life gain effects is the answer. Search your collection for good Lifesteal keyword units or implement a strategy to beat then before they burn you. There is no other way.

Quote From Sykomyke 

The only time mirror draws every saw the light of day in hearthstone were "mill" decks, and you saw how Blizzard handled that. (nerfed)

While its true it was mostly played in mill decks, Oracle also saw play at least in another 4 situations:
1- Tempo Rogue; (open beta)
2- OTK decks: Exodia Mage and Lerroy Rogue;
3- Fatigue decks: Warrior/Priest;
4- Included as a tech card to mill combo pieces of Exodia Mage, Aviana Druid, Handlock and Dead Man's Hand Warrior.

My thoughts about the deck:
Requirements: Maokai leveled up, 5 dead cards in hand, 13 mana available, all 3 copies of Veteran Investigator, Splinter Soul must not be disruped, opponent must not have ways do shuffle cards back into his deck.
Those conditions are VERY HARD to fulfill.
By the time this deck can pull off that exact exodia combo, other decks should have plenty of time to end the game already.

About your question:
Against aggro, i think there is not much difference. While Veteran Investigator has a body to contest the board, giving away an extra card helps them to find finishers/lethal a few turns later. Pilfered Goods is just plain useless in this MU. Owning minions versus spells to contest the board should be pretty even.
Against combo and control, Pilfered Goods have at least a chance to disrupt/delay plays and its not dead, while Veteran Investigator is not a card we want to play outside of the combo as it  also helps our opponent to win/snowball faster.

Quote From OldManSanns

Compare it to Braum: he's less than half the mana, regenerates, and he can challenge so he even helps on offense, yet he's one of the least-played champions because zero attack is just so bad.

Braum never saw play because he can't block Fearsome and Elusive units. It has nothing to do with his 0 attack.

I just defeated this Nautilus deck with Purrsuit of PerfectionBADCARDNAME hahahahaha

Seriuosly, the deck isn't that great

All cards work. Even Single Combat.

I've been facing this deck a lot in my ranked games and i think i only lost to it twice, both times due bad luck (didn't get my finishers or The Ruination)

Quote From Cronkonium

... Teemo which can seemingly be played 3 times in a row in decks of cards 40 & above. 

Very interested to hear how one can play a deck over 40 cards from the start.

Noxus has the best anti-Teemo cards including:
Blade's Edge, Death Lotus, Culling Strike, Whirling Death, Death's Hand just to name a few.

Captain FarronBADCARDNAME is designed to teach new players the concept of finisher cards.

Farron is easy enough to fit in any deck as a stand alone win condition. Replacing the hand with Decimate is a very powerfull effect indeed.
It will put pressure on the opponent to win the game in the next few turns or be overwhelmed with direct damage.
This "preassure" is also know as Win condition / Boss card / Finisher. 

Farron is strong but isn't overpower at all.
First, Decimate costs 5 mana. While it puts preassure, it will take multiple turns to play all Decimates.
Second, the hand will be filled but nothing then Decimates. That means the player is now commited and won't be able to react to anything on the board.
Third, Decimate has SLOW spell speed. In tight situations, when both players nexus are low, the speed matters a lot. And those spots happens very often.

Conclusion: Captain FarronBADCARDNAME is just an introduction to finishers. Easy to play, doesn't require other cards to work and can fit in almost any deck. The downside being the slowest one to close games when compared with all other finishers.

Edit: The video above posted by OldManSanns illustrates everything stated in my post. Worth a watch.

Quote From OldManSanns

1. EVERYONE was playing decks built around expansion champions, implying they heavily crafted immediately
2. All my pre-expansion decks are very weak against these new decks:

• • My P&Z/Noxus aggro deck and SI/Frejlord control deck were both winless for the night. 
  • I finally had some mild success with Vlad + Braum of all things--still less than 50%, but at least I could grind out my bonus XP

 

There was enough time to theorycraft decks before launch. Once the expansion hits, isn't getting the available rewards then use those to craft and have fun the standard thing to do? 

P&Z/Noxus Darius is EXTREMELY strong if you include a few expansion non-champion cards. 
SI/Frejlord is the deck i am still playing in ranked and destroying the majority of new decks, as i am taking advantage such decks are still not optimized.
Warmother is sadly another history. It didn't receive a single useful card from this expansion, so its pretty much dead.

IF new players are getting stomped, its a match making related problem and nothing to do with the expansion.
Don't forget players also have the option to grind quests against the AI and friends.

What really doesn't make sense is Teemo not having the scout keyword.

I mean, his title is THE SWIFT SCOUT and literally has a line: "I 'll scout ahead" ¬.¬

Just did some playtest on Unyielding Spirit 

Some interesting facts:
   1- Etheral units cannot die anymore;
   2- Kill effects that requires the target to die still resolves but won't kill the unit. 
       Example: Glimpse Beyond draws 2 cards without killing the target, but Chronicler of Ruin does nothing;
   3- Both Detain and Will of Ionia work as expected;
   4- Playing Detain on a target with Unyielding spirit is almost a death penality;
   5- The target doesn't take any damage but retains the current HP if damaged prior the cast. This is important when
       blocking against Overwhelm units.

Let's not forget Judgment played on Fiora can potencially win the game right away while Unyielding spirit will take a couple turns.

I believe one big reason behind the cap on champions is for the oponnent to have a guess on what kind of deck he is about to face even before the mulligan phase.

Not sure how annoying flying creatures are in MTG, but Magic has a few saving graces:
1- All collors have flying units.
2- The creature needs to tap in order to declare an attack, so it won't be able to block next turn unless its untapped;
3- At least in my days, saved a few problematic creatures like Hypnotic Specter, flying creatures were a bit too cost-expensive in general to be abused;
4- MTG has board clear spells from T4;
5- Floodgates;
6- Ping effects.

While its true both concepts share some similarity, LoR elusives are far worse given the limited tools to play around it.

Solving the elusive mess is not a job for one person alone.
My objetive is to brainstorm some thoughts in hope someone could polish or spark new ideas to adress the issue. 
Thanks for your reply, healthy discussions like the one we are all having on this topic are a step in the right direction.

About your answer:

1. Its usually how every company deals with problematic cards other then ban. Not the best way but easy to do. 
   Buffs on elusives are strong since the stats it generates also gets the keyword elusive. This interaction will never be balanced without printing cost-effective removals or effects that "remove all text and keywords" from units.
   So yeah, i agree only changing the cost alone without the support of other cards won't solve the problem.
2. I fully agree, but at least is better then what we have now. 
3. Very likely. 
4. Yeah, its intended to make elusives weak versus AOE spells. This would greatly increase the risk of playing multiple elusives in a single deck.
5. Elusives can block any units. The new concept is that elusives could not block non-elusives. This would make pure elusive decks much weaker against other aggro decks.
6. The original idea is to spread the keyword "ward" in many different units already in the game. Its not meant to be build around it. It should be done in a way most decks would end up with 3-5 ward units on average without tech.
7. This solves the elusive problem but its very dangerous to other cards like They Who Endure.
8. Yeah. This is much better then number 7 as stealing keywords doesn't screw big followers as much;
9. Its an improvment thou is slightly iffy: the keyword would need to explain that the effect only works while attacking.

Here are a few ideas on how to fix elusives:

1- Make elusives cost-inefficient;
2- Elusives lose the keyword elusive after a block/attack;
3- Elusives go back to the hand after a block/attack;
4- All Elusives have 1 HP;
5- Elusives can only block other Elusives;
6- Print a new Keyword: "Ward". Ward -> The unit and adjacent units can block Elusives;
7- Print situational spells that remove the Keywords: Elusive/Fearsome/Overwhelm.
8- Print units that can steal/remove Keywords;
9- Elusives can be blocked by any unit but they don't receive combat damage from non-elusive minions.

My favorite is number 9

Note: A fast healing spell on the target can negate the damage.