Full timing, you'll most likely be on the high side of the trailer's carrying capacity. Your actual trailer weights will be pushing the 7220 GVWR and actual hitch weight will be over 900 lbs. When you add the weight of a weight distributing hitch and anti sway equipment, your truck will need enough payload to support 1000 to 1100 lbs of trailer weight, in addition to the weight of any passengers, cargo, or aftermarket accessories, that may have been added to the truck.
Read the fine print in many tow vehicle owners manuals, you will see something like "the vehicles max towing capacity is limited to the weakest link in it's overall tow ratings". The weak link, in many cases is payload.
You mentioned "dealer added" tow package. That would make the tow package an aftermarket accessory, and doesn't necessarily increase anything in regards to towing. In fact, the added weight reduces available payload, by an amount equal to the weight of that added equipment. Example: Say the truck came from the factory, rated to carry 1400 lbs and tow 7000 lbs. After the dealer adds 200 lbs of towing equipment, the vehicles remaining capacities would be reduced to 1200 lbs carrying and 6800 lbs towing.
Will that 1500 GMC pull that trailer, probably. Will you (or the truck) enjoy the ride, probably not.