As long as the propane isn't over-filled, empty or full doesn't matter, but since they have propane where I buy gas near home I fill it up before winterizing so it's one less thing to do before heading out next time.
I try to start the gas winterizing process with about 1/3rd of a tank of gas. I then add enough Sta-bil to just slightly over-treat the soon to be full tank of gas. Then I start the generator and run it long enough (under load) to be sure to thoroughly treat the generator. Then I fill the Motorhome with gas and drive home. This ensures the engine is treated too.