If you do as Bosunsmate suggested, that would be a great idea so you can run the motor and get the fuel with your stabilizer thru the entire fuel system, and get your fogging oil in if you are intending on fogging the engine (I always do it for the winter months, but some guys don't unless it will be stored for a long period like a year or two). When you shut the motor off and get rid of the garden hose off of the water pickup tube, the head will drain fully again, just as it would with the LU in place, even faster and more thorough.
edit: I personally do not know how to tell the pickup water tube from the discharge water tube, but you need to put the hose on the right one. Maybe someone can chime in here so I can learn how to tell the difference. Thanks.