I've used the loaders. Got it. I know how to flip a shot gun, everyone does now that is was in a wick movie.
Only issue I have with what you said is that the chamber should be loaded first, not last. But hey, these guys play for fun and prizes, not life and death.
On almost all shotguns (less some Brownings and those with aftermarket Autoloader kits) when they run dry the bolt locks back and the loading gate is locked in the down / lower position (so cannot access the magazine).
For competition (where you are on the clock) it is most efficient to load the chamber first (typically by dropping a round in the ejection port) and then hitting the bolt release which will then let the loading gate move / give access to the magazine tube.
If you prefer you could drop the bolt on an empty chamber and then load the magazine and rack the bolt. Seems inefficient to me.