The GCWR of that truck is 20,000lbs. - You would be cutting it VERY VERY close on a SRW model - on a DRW you would have a little more margin, but not much.
Our 38FLSA loaded is right around 16.5K to 17K (2 people, for 9 days or less)
2015 Sierra Denali 3500HD SRW
2015 Jayco 38FLSA - Loaded -
B&W Companion 20K slider hitch