I can give you some insight into an older Tahoe (2003 LT) with the 5.3L and towing package. I weighed the trailer (~6000 fully loaded) and the combo of trailer/Tahoe (11780), and was well under the GVWR of 13400 for the Tahoe. The max tow rating my Tahoe is 7400 lbs. I think current ones are in the same range, maybe up to 8000. I have a good WDH and the air shocks in the rear.
I've towed a lot in the mountains. My Tahoe and trailer bog down at higher elevations, once I get to 10000 feet, I know it, and if the grade is steep, I'll slow down to <30mph in 2nd gear. The Tahoe has the strength to do it, it's just not fast. On less steep grades, even at elevation, there's not as much of a problem, but it's still slower going.
On the flats, however, it's another story. I've made the trip east to Indiana and back and it's a fine combo. Averaged ~9mpg at 55mph. The Tahoe is a comfortable vehicle for long trips and the trailer is barely noticeable.
If you're staying in the flats, it should work for you. That said, the weight of the loaded trailer will be a strong determinant if it will work for you. Frankly, I would not go much more than that 6000 lbs fully loaded that I have in my trailer. If the newer Tahoe has a limit of ~8000lbs, I still wouldn't go much more than 6500 lbs on the fully loaded trailer.
2007 GMC Sierra SLE 3500HD Dually
2016 Coachmen Catalina Legacy Edition 243RBS
2007 Keystone Outback 25RSS - R.I.P.