YES, you can hook up the hose to the seadoo and have them run for up to 5 minutes. Connect the hose and start the seadoo. Turn on the water after it is started. Turn off the water, than shut down the seadoo. This way it won't allow water to back flow into the engine through the exhaust due to no back pressure from the engine not running. The bearings and seals on the impeller jet pump, are cooled from being in the water. When it is on the trailer it doesn't have that cooling effect so they will get hot after about 5 minutes.
I pre start my seadoo's too, dry before I leave for the launch too. Just for a second or 2 to be sure it will start at launch. Peace of mind is worth lot.
I'm glad you got the dess to work for you. I think you were running out of options. It's hard to see everything your doing from just being on the forum...and not being there.
Karl