Rooms are usually assigned a few days out, whenever possible, so it shouldn't matter the time of day you check in. Your request should be noted, and if there is a room with a King bed available, hopefully it will be assigned to you. Best you can do is ask at check-in and if a room with a King Bed is not available then, let them know if you are willing to switch later in your trip.
I use to believe in this but having always stayed club level I would think this is true. However our stay this past June was NOT club at YC and I too worry that the good rooms are gone. I checked in at 11 AM not counting on getting a room. The nice CM said "lets see whats available" and gave me an upgrade to lagoon view.

I personally believe the earlier the better for check in b/c if someone doesn't like their room they will request to be switched and I won't be there to have claimed my room.