The answer is yes, with precautions. The standard bed is 6 and 1/2 feet to the tailgate, so YES, the gate would be down. You can reinforce this with an 8' long section of 3/4 plywood that will distribute the weight off the fragile tailgate. The trailer hitch
may have some clearance issues with the tail gate in the down position, so your trailer tongue will need to be LONG, and a tongue jack (if you use one) will need to be placed on the tongue BEHIND the tailgate in the down position. Check trailer interference with the tail gate in all cornering positions and going up and down ramps. With a little caution, should be no problems.The vehicle will be close to the rated gross weight. You may need airbags (ride-rite) to keep the headlights out of on-coming driver's eyes at night. But the vehicle has PLENTY of power and brakes to handle this load, in my opinion.
If you have a long box then yes it will fit in the box but the tail gate will not close so load it with out the tailgate on . If it is a short box then you will have to have the rear tires on the tailgate. I would think would also have issue with the tailgate hitting the front of the jetski without the use of a hitch extender. and then of coarse there is the tailgate issue as well if your truck is under warranty then it's not much more then a saftey issue loading it in there. I have loaded my quad with the tracks on using the tailgate with little issue but it only weighs about 1000lbs with tracks.