Yes you can. Our family has pulled 14K lb livestock trailers since the 60's with 2500-3500 pickups. Only recently did we get a diesel, only because GM stopped offering manuals, so we ended up with a Ford. A 77 Gm pickup had less HP, worse brakes, and about the only thing it has is weight. Will you be pulling it at 80 up a 6% grade? No. But you didnt do that until the 7.3 powerstroke or 24V cummins came out. Is there a difference between a 70's 2500 and a late model mid sized SUV? Yeah, the late model SUV isnt a POS, haha. People are WAY over exaggerated when it comes to towing. Back in the 70's people pulled combines from MN to TX with nothing more than a 345 2bbl IH gas grain truck. Those had probably 170 HP and 300 ft lbs on a good day. Thats in a 25K lb truck pulling 40k lb trailers. With sketchy drum brakes. Why people decided they needed 800ftlbs to pull around their skiff is beyond me.
I bought my Rainier to pull my cars around and have no worries. Havnt towed anything yet since I just got it but its MORE than capable. Brakes are the same size as the same era GM pickup (if not better, rear disks), same trans, same engine (if you have the 5.3), even if its a I6 it still has 270HP. More than any 1500 pickup until mid-late 90's. Drive a little slower if you need to. What did somebody in 1994 do if they had a 1500 pickup and needed to haul a car? They just did it. An 06 denali is more of a vehicle than a early 90's pickup.