The problem is that every truck is different. Just because I can fit 32's on this truck with a 4" lift doesnt mean that you can too. The fitment chart is pretty close, but not 100% accurate for ever truck. Is it street truck that will never have the suspension flexed... you may stuff 33s under there and never rub. How worn are your body mount bushings? If they are worn out, the body might be sagging a little and you'd need a 4" lift just to fit a 31".
BUT, the chart says you need a 4" lift and some trimming to fit 32's. You're asking if you can fit them with just a 3" lift and no trimming. Come on, what do you think? You're not stupid.
Now, actual tire height and width will make a big difference. As will rim width and offset. I would plan for a 4" lift and see how they fit. Maybe you will need to trim, maybe not. You may get away with just some washers on the radius arms to push the axle forward a little. Maybe you'll need a 1" body lift. Like I said... Every truck is different.