We have a 2010 Suburban that is probably pretty similar to your Tahoe. I use t/h every time the trailer is hooked up. I leave the truck in D most of the time, unless the transmission starts 'hunting,' which means it is shifting up and down too often. My truck almost never gets into 6th gear when towing -- it is in 4 or 5th most of the time. However, it is pretty good at avoiding hunting too much. Perhaps ironically, I get more hunting on apparent flat surfaces than I do in the mountains. Out in the flats (most land out here is not truly flat, of course), a gust of wind or an overpass is always enough to kick it out of 6th, and maybe down to 4th. When going up hills, it seems to do a very good job of holding the gear.
Note that when it is shifted out of D, the grade braking feature does not work, and you'll have to downshift manually to slow.
