I've got a Hat Champ, although I have to admit that I haven't messed with it much.
I've printed hats with it, but they were low profile ones.
Do you have the larger platen for the trucker caps (for your Hat Champ) ?
You'd definitely want to use the big one. Once the hat is locked in place, you should be fine with multi color and with the trucker caps, you've got a bigger printable surface, so that's good. You should be fine. Just don't rush the set up with it.