I think that the way how it is currently expected to be implemented makescreates a wide open door for abuse.
ProposedThe proposed design makes it possible for anyone to create a hundred sock puppet accounts and immediately cast "likes" in any quantities they want. And this kind of violation would be much harder to catch than voting-fraud. And even if caught, what are you going to do? Suspend the (1-rep) abuser? Ha, they will just create the next hundred of sock puppets and keep doing what they did.
Be prepared to observe totally weird things like poor quality / spammy answers (including, but not limited to, all kinds of rants and senseless jokes) sitting at -10 score and having thousand likes.
Heck, be prepared to observe this even without any abuse, from legitimate "thankers" (which will be even more painful because there will be no way for you to stop that, no. There isn't any reason to suspend them and undo the damage).
You know, even upvotes from 15-rep users may be harmful (give a read to Atwood's Trouble With Popularity if you haven't yet). And now you are going to multiply this risk by 10,000.
The idea to reduce useless "thanks" in comments looks tempting and in theory I could support tricks helping in that. However, the price we have to pay for getting it the way you suggest seems too high.
You know, my primary reason for visiting Stack Overflow (explained eg here) is to learn from properly (cu)rated content, and thinking about how post quality rating may get totally skewed... it just makes me sad. Very sad.
Consider implementing this in a way that carries less risk of damaging content rating. One thing that comes to mind is to somehow limit visibility of these "likes", for example, showing them only to those who cast the like and to the post author.
Another thing I would strongly recommend to have is public visibility of likes in user profiles and (especially!) in Data Explorer. This way you could leverage power of broad site community to discover and fight potential abuse.
In order to minimize impact of possible abuse, I would additionally recommend that user deletion would make all of their likes disappear - immediately and unconditionally. For the same purpose, consider implementing "likes invalidation" tooling similar to one that is currently used for invalidation of fraudulent votes.