Since no one has commented yet, I'll tell you my opinion even though I don't have your truck set up.
If your not lifted I think you're going to rub the fenders and the upper control arms.
I've only run that large of tire on a gasser truck but it had 4:10s. It was a great match! You'll always lose some low end and mpg with each increase in tire diameter but with cummins power and a manual trans, i think it will be minimal, particularly with 4:10s. UNLESS you tow heavy frequently.
You may notice you need to relearn the rate you lift the clutch pedal.
I'd personally be more concerned with rubbing and my suspension handling the extra unsprung weight and if i towed heavy I'd opt for a bit smaller shoe.
37's look really sweet on your truck. I've ridden in just one 3rd gen with what appears to be your set up and 37's and the owner actally said the extra diameter seemed to smooth out the torque curve. I can kinda understand that, although what he was really feeling is the slight loss of low end your worried about. the truck did not seem to labour at all. I liked it.
Good luck, jeff