Is there a limit on how good you can get at Hearts?
I just want to say, as a mathematician who has studied Game Theory for several years, that you DO NOT need perfect information to have an optimal strategy.  In fact, Game Theory has a very rich body of results about games of imperfect information.

It is a common misconception.  Here's another one: an optimal strategy means you win every time.  This is also not true.  An optimal strategy is one that maximizes your expected payoff.

Now that that's out of the way, I want to commend the questioner on a great question.  I was actually just googling this question myself, trying to see if any journal articles have been written about it (I was thinking about doing a game-theoretic analysis of Hearts for a thesis paper).  I haven't found anything yet.

Like most nontrivial games, Hearts has a HUMONGOUS game tree.  There are 52!/(13!^4) hands that could be dealt (each of the 4 players gets 13 cards).  That's just how many nodes there are at the second level of the game tree.  Each of those nodes has a huge number of branches (the number of branches at each of those nodes is the number of ways four players can choose three cards from 13).  Then each of those have yet more branhces, and so on.  Even a rough calculation shows that there are far more nodes in the game tree than there are atoms in the known universe.

So using Zermelo's algorithm to "solve" hearts (though theoretically possible) is - in practice - not possible.  So much more sophisticated techniques must be used.

If you want to write a computer program to play near-optimal Hearts, I would suggest using random samples and Markov-type simulations to estimate optimal moves.

In short, yes, optimal play does exist.  But it could be very hard to find without some pretty slick game-theoretical analysis and/or a lot of computational power.

I hope this helps.  :)