No! Never run the motor of your watercraft out of the water. While your Sea-Doo’s ROTAX engine features a closed-loop cooling system, similar to that found in an automobile to ensure a consistent, debris-free source of cooling liquid, that liquid is cooled as it’s passed through internal channels in the craft’s ride plate, the rectangular metal plate covering the jet pump. That plate needs to be submerged in the water in order to dissipate heat and ensure your engine’s cooling supply stays below a specific temperature.
The only exception should be after riding in salt water, to flush out the engine, but make sure you don't run the motor for more than 30 seconds!
To keep your engine, exhaust and other components cooled and running properly, never run your craft out of the water. And when in the water, never start your craft in less than three feet of water depth. Any less and you risk sucking up rocks, sand and other debris that could damage the impeller and jet pump components, or clog vital cooling lines.