To answer your question you have to consider what causes his hesitation. That could be one of his tragic flaws. Does he hestitate because he is cowardly? Becuase he over-intellectualizes? Because it goes against his moral nature? Once you decide then you really have the answer to your question. His hestiation is the result, not the cause.
I would argue that Hamlet fits some of the qualities of a tragic hero, but I think Shakespeare wants to make Hamlet more complex than that.
Hamlet fits several of the characteristics of a tragic hero--he's born into nobility, he is well-liked, he meets a tragic demise. However, I don't know if you can argue that it's his hesitation or indecisiveness that causes his downfall or that he has a tragic realization. Usually, a tragic hero realizes his fault and that his tragic demise is a result of that. I also don't think that Hamlet has excessive pride, a usual characteristic of a tragic hero.
Hamlet's hesitation doesn't necessarily cause his downfall. True, if he had just killed Claudius when Hamlet first realized Claudius' guilt, Hamlet may not have met his own death. However, there would be less of a play or it would not be a play about Hamlet proving Claudius' guilt and deciding what to do with it.
Hamlet also deals with other conflicts, not just in regards to Claudius. He deals with his love (or lack thereof) for Ophelia, his relationship with his mother, his friendship with Rozencrantz and Guildenstern and their betrayal. Even though Hamlet may seem indecisive, he puts different plans in motion to make sure what he is doing (killing Claudius) is justified.