When you do online check in, it asks you what time you'll be arriving. In 3 trips since online check in started, by room was ready each time (12:30 - 1pm). What room you get depends on the requests you make when you book your reservation - not how or when you check in!
I did online checkin again for this Friday, although since it's for Jambo House concierge it was probably a waste of time. But, they know I'll be arriving at 1pm so perhaps my room will be ready again.