No. Not if the infinite collection of universes is arranged in such a way such that you go up against successively more and more skilled competitors. If so, the probability of success on a given iteration could go down each time. If it goes down fast enough, the probability of success in the limit can be less than 1.
I don't think it can go down forever. There's some nonzero probability of quantum tunneling directly to the treasure before anyone else has a chance to do anything.
Also, I'm not sure what Kin is trying to say. Either there's a finite number of universes, and you'd just finish last, or she doesn't know what "infinity" means.
The current Goblins Comic is relevant.