Depends a little bit on the tire. If you are at stock ride height, you might get a little rub on the front mud flaps at full-lock turn when the front suspension is compressed.
I had a Toyo AT tire 265/70/17 when I was at stock height, and that is the first place they will rub. These tires have a rather square outer edge on them, so if your potential new tire has a rounder edge, then you might not see any rub at all.
I had a set of Michelin LTX M/S2 265/70/r17 on my 2003 Sequoia Limited. At full lock, they would rub on the frame. Not a big deal, though; wore off maybe a couple square inches of paint on the frame, but no damage.
I am running 285/75R16 on my 2004 SR5 Double Cab. So my tire size converts to 33" x 12.50" vs your size converts to 31.6" x 10.4". I do have a leveling kit on the front though. These tires rub on the frame at full lock, but no big deal, either don't turn at full lock or just let it rub.