You may want to check your numbers on payload, GVWR, tongue weight, etc.
Many of the posters saying go for it, are driving 3/4 and 1 ton trucks. They have plenty of payload to carry their tongue weight and have stuff in or on the truck bed. I too, say go for it, if you have the capacity to carry the weight. You are talking about 3 - 400 (maybe more) extra pounds, with cap, generator, bikes and chairs, etc.
My previous setup was a Nissan Titan (with a 200 lb cap) and a 30' TT. When I added the weight of my trailer tongue (950 lbs), WD hitch, the cap, myself, and my wife, my payload was almost maxed out. Another passnger or a generator would have put me over. It was a good excuse for mother in law to not ride along.