If the truck has been equipped with a proper suspension lift kit there really won't be any adverse effects to the towing capacity. However, I have seen some hack jobs that I would worry about even not towing a trailer. The larger tires will have an effect on the final drive ratio, however, with it being the diesel it is less impactful on the overall performance. In extreme scenarios I have regeared a few for friends but the common gear ratio that GM uses in its trailer towing package with the Duramax option is 3.73 and it seems to be a nice compromise for daily driving as well as towing. Also keep in mind many of the newer ones are coming with 20" wheels now and have been coming with 18" wheels for some time. The old days of 16" wheels on 3/4 and 1-ton trucks are a thing of the past. You didn't mention the year of truck you were looking at so I am assuming you are talking about a lifted truck running oversize tires.
That being said, make absolutely certain the tires are properly spec'd with the load range "E" (10-ply) tires to ensure load carrying capacity is not effected. Some wheels can have a lesser rating than the OEM wheels but most are at or better weight capacities than the OEM wheels.
I have a 2006 2500HD Duramax that is lifted 6" with an RCD suspension system running 20" MKW wheels with 36" BFG All-Terrains on and up until this past spring have been towing a 26' enclosed race trailer for the past 8 or so years now. The trailer weighed approx. 12k pounds and one thing I have noticed is that with the somewhat lower profile tires than my previous truck (due to the larger wheel combination) is that it is much more stable running down the road. In my previous truck running 33" tires and 16" wheels, in the curves it felt as though the trailer would try to "push" the truck through the curve using the mass of the trailer. The truck was trying to "lead" it through the curve yet the trailer was trying to push it straight. With this truck running the lower profile tires it is rock solid going through the curves on the interstate at speed, very stable on two-lane country roads and also very easily maneuverable in towns/cities. The trailer was loaded the same for both tow vehicles but I would rather tow with my current truck any day of the week vs. my last one with larger sidewall profiles.
On a side note, I will add that one thing I pay particular attention to is the unit bearings. The larger tire/wheel combo will place more stress on these front unit bearings and they can have an earlier failure potential due to these heavy tires/wheels exerting more stress on them. I say potentially because I have seen these GM front unit bearings go for well over 100k miles on trucks and I have seen them fail on a couple at less than 60k miles on a non-lifted, stock truck. I check mine regularly and accept the fact that they will need to be replaced sooner due to my large lift and oversize tires but I am willing to live with that. I currently have 88k miles on my OEM bearings and have been running the truck in this configuration for the past 50k miles now since I have owned it. I just thought it would be worth mentioning to keep an eye on the front unit bearings. I also keep a closer eye on my brakes with the larger tires and wheels due to the leverage they induce into the drivetrain but I have not noticed any adverse effects there either.
That has been my experience towing with my lifted 2500HD Duramax.
Mike.