Yes.......
Yes.....you can start the ski and run it for a minute or so without even hooking up to water.
But the procedure calls for you to start the motor, then turn on the water. And shut down in the reverse order. That's to keep water pressure from forcing it's way through the "0" rings.
Oh, hooking up the hose. If you don't have a hose connection already on the ski, then you can go to the auto parts store and get one of those radiator flush out kits and where the water inlet from your pump connects to your head cover, break that line in half and install that "T". Then, you'll have a place to hook up your water.