Perhaps my motor is different from eneryone elses on the planet, becuase I seem to defend this pretty often.
My Yamaha F115, flushing on the hose connection, leaks water all over the place. (See pics.)
In the first, you can clearly see water coming out of every orifice in the lower unit (and there're a bunch of them.) In the second, you can see water flowing out of the water intake screens, and the prop hub. Proof that water does flush out the input and pickup tubing.
The cooling system does not have a one-way valve or anything that will prevent water leaking back down; the impeller spinning drives water up through the head, but if it's not spinning, it won't prevent water from flowing back the other way. If it is spinning, but water is insufficient to fill the chambers between the vanes, you will get lubrication but no pumping (impellers are an eccentic vane, decreasing volume type pump.) There may be some chambers within the impeller/housing that won't get flushed if not running the motor, I suppose, but given that the manufacturers don't consider this a problem should be a little telling.
I'd be interested in seeing pics of other motors running on the hose connection (engine off.)
p.s. Ignore the green hose in the background; that used to be a garden watering hose that has now become my dogs plaything. She's busy cutting a 50 foot hose into 1 foot sections, in between dragging the rest of the hose around the yard. You can also ignore the yellow tub. Impromptu water resistant (hah!) storage.