So much depends....
Mainly where you will towing and how you drive
Struggling would be my expectations with head winds and hills. Some won't think so, but it would not be pleasant for my style and/or expectations of driving
An external ATF cooler is part of the tow option.
GMT900's have a welded on receiver and is NOT removable....it is the bumper's main structural member....in...addition to being the receiver. Also limited to a WD rating of 1k lbs
Best to load up with EVERYTHING as if going camping and weigh it. Suburban's surprise most, as they can hold so much. Am hoping yours is the exception...as most in your situation end up very close to their GVWR without hooking up....on that, a good thing you are going to upgrade to the next higher class tires...especially if you will be both close to your GVWR and towing on top of that
Good luck
PS....I have driven several GMT900's and do know them well enough in comparison to the GMT800's and GMT400's I've also driven