Can fruit juice be used to hold a cheesecake crust together?
I've experimented a bit with liquid flavorings in tart crust (not specifically replacing butter -- I still had butter in there) and I find that it does tend to make the crust soggy, but if you are baking the crust first, you can cook it longer to counteract this and it comes out a little more like shortbread. I don't think I would recommend it, and I actually try to keep as much room-temperature liquid out of my crusts as possible.

On the other hand, one of the most famous NY cheesecake places, Junior's, uses a spongecake base instead of a traditional crust. If you really want to add peach to the crust, maybe you could work off of this? Maybe replace one of the eggs with pureed peach? (I was surprised and pleased to find that Epicurious has the official Junior's recipe online, actually.)

Another option would be to keep your normal crust recipe and put a layer of peach jam or compote on top of the crust (if you have a baked crust, or even the sponge cake method). You would want to make sure there is as little liquid as possible in this layer or you're still going to have soggy crust.