Normally, no. Not if you adjust your air pressure accordingly. BUT, there are always exceptions of course. Other memebers here I believe have said that they experienced wierd wear and handling characteristics, but I never have. And most of the tire manufacturers list 8" through 10" as optimum for their 12.5" wide tires so I'm sure it's not a common problem or they wouldn't list it as an appropriate combination.
There is really no discernible difference in tire height with the different rim widths, and it's hard to measure any difference in overall tire width either. The main difference is not that the tire actually bulges out on the narrower rim, but that the rim is narrower, causing the tire's bead to roll in slightly, making it visually "bulge" out, keeping the rim's edge farther in and better protected from rock damage.
I ran a set of 35x12.50 General Grabber M/T's on 15x8 wheels on an IFS full-size truck with 6" of lift and got 67,000 miles out of them and they handled great. I would've gotten more from a tread-wear perspective, but they finally started pulling and following too many road grooves so I got a new set even though they had quite a bit of tread left.
So as far as wear is concerned, "every truck is different!".
Paul