Yes full size spare fits in there just fine. In the case of ours with the factory towing package it came with a full-size-full-life spare on a 17" steel rim, the jack and its accoutrements live in that space under the spare so nothing to gain from flipping it in my case as the space is used. Your situation may be different I don't know what you got with yours, some come with no spare at all, some have a temporary use donut spare, some have a full-size-full-life spare. If you didn't already, you will have to put the floor piece at its highest setting is the only difference.
I bought a set of 17" trailhawk rims and factory tires from a member here to switch over to for a couple years (the continentals on our 18" stock rims are getting pretty wore down for handling a Minnesota winter). I bought a good condition used wildpeak to match and had it installed on our 17" steel rim so they can all be exact matches if I have to use the spare. It fits in the same spot just as easily as before, even though the wildpeak is taller than the original tires on our non-trailhawk. You could easily fit a 30" tire in that space by the looks of it.