I have no question that it would do the job fine, however that rear end, towing in hilly terrain I think you will not be happy with it.
What transmission does it have? If it has the 8-10 speed that will make a big difference, but I still think you would be happier with a more towing appropriate rear end.
I own the next closest thing to the combo he's looking at, and I DON'T think "it would do the job fine." I've never seen the 10 speed transmission paired with a 5.3 - only the 6 speed, but could be wrong. Have you actually owned the combination, or are you guessing? I own a 5.3L with 6 speed transmission and 3.42 gear,(part of the towing package from GM) and would not want anything less torque wise. It already drops the MPG from 21 to 12. I believe the 3.23 would be in near constant strain, making fuel INeconommy even worse.