I used to tow tow with an '03 Trailblazer, I6, 3:42, 4WD EXT. My towing capacity was 4900#. But...
First things first, ignore the dry weight. No one tows anything at the dry weight. Once options are added and his "stuff", it's a fair bet that trailer will weigh 6500#+ with an 850# tongue weight. Those are the kinds of numbers you have to think about.
Also ignore what the online sources say. Get it right, this is too important to guess at. Everything he needs to know about that truck's exact specs is in 3 places, his owners manual, the RPO sticker in the glove box, and the weight sticker in the door jamb. There were 3 gear sets available for GMT360/380s, look for one of the following RPO codes: GU6 = 3:42, GT4 = 3:73, GT5 = 4:10. Very few I6s had 4:10 gears. Most have 3:42s.
Towing capacity and payload are also determined by 4WD vs. 2WD, and EXT vs standard length. The payload of that truck is likely less than 1100#. Assuming a loaded tongue weight of 850#, that leaves about 200# for his family and their stuff. Not much room for anything inside the truck. I believe the GCWR is 11000#, but again, the owners manual has the most accurate information on this.
BTW, the W/D limit of the hitch is 970#, DO NOT go by the sticker on the hitch. That's for the hitch itself, not considering the vehicle it's attached to.
We towed our X20E with our Trailblazer for one season. The X20E has a GVWR of 4750#. Yes, it "towed fine". But it got about 8mpg (our Sierra gets 10.5 or so towing the same trailer), struggled in the wind, and no way would I have towed with it on longer trips or in mountains. It was at the max I would ever consider towing with a Trailblazer. Your friend's trailer is going to be about 2000# heavier and is several feet longer than my X20E.
We sold our Trailblazer in part because it had a lot of miles on it, and in part because it was marginal at best for towing our X20E. Towing our trailer with our Sierra is a real pleasure. Rightsizing your trailer/TV combo makes all the difference in the world. BTW, our Trailblazer was great when towing our old Kiwi 17A, a 3500# GVWR trailer.
So all in all, I see this as a really bad combination. Set up properly he'll be safe if he does short trips on mostly flat terrain. Anything else will be an unpleasant experience at best. He'll be replacing that Trailblazer in less than a year.
2013 Jayco Jayfeather X20 E, 2008 GMC Sierra 1500 Crew Cab Z71 SLE