A big class of imperfect information games can be modeled by having a record of everything the agent has seen so far. Then it has exactly the same, if not more, information available than a human player in the same position. We know that with equal information AIs can make better decisions than humans (see also, AlphaGo :] ) so at that point the AI could reasonably be expected to achieve superhuman performance.
The "imperfect information games are harder for AI" crowd are going to be surprised by just how badly humans deal with imperfect information. AIs have a much better memory than humans do, and much more potential to use actual probability which humans are truly shocking at utilising (although neural networks don't seem to utilise this edge; so far).