Yup, I have a 35x12.50R15 BFG MT under mine; but there is no hitch and there is very little clearance between the spare and the rear stabilizer. It hangs down too low, IMO, and I plan to move the spare to a bumper mounted carrier when I can afford it.
I was wondering if I keep a stock tire there for emergency and would be able to put a flat 35" tire up there. I do have a hitch. I like to get in the back quite often and to have to move the tire out of the way seems like a pain. There is no perfect solution have to weigh the pros and cons.