Will these tires tuck???

My truck has what seems to be some pretty big tires on it, and I'm wondering if they are going to tuck. The tires it has right now are 235/85-16 all around. Am I going to have to get new tires after a SFBD and getting my bags on?? I'm planning on bolting on some 22's at some point. Would I be better off making everything work with these tires so the 22's will slide on without a bunch of extra work??
I forgot to mention that it's the truck in my sig

As for height they will work but the 22s will sit outside the rear dually fenders.

thanks man