We filled out the express check-in for the first time on our 9th trip in July. This is the only time our room was available when we arrived (around 10-11 am). Coincidence? Not sure, but we will be filling it out in the future every time just for a chance of our room being ready when we arrive. We have been premier members for 7 trips, so premier status doesn't have anything to do with the room being ready.
It definitely helps a bit because paperwork lined up behind desk and they grab that quickly, to then start the checkin process - doesn’t hurt to save a bit of time to get you out to that sexy pool even faster!
I like the way you are thinking!! Hell, we are even wearing our swimsuits on the plane in anticipation of having to wait for our room...