What day of the week are you arriving? Saturday and Sunday are busy check out/check in days and whenever I have arrived on either day, my room has not been ready until closer to 2pm. I will say that the more general your room requests are (or better yet - no room requests) - the more likely you will be to get into your room earlier.
Based on previous conversations I've had with CMs, I've been told that when rooms are assigned for those who have checked in online, they try to get them into rooms that will be ready based on their arrival time. Room requests are looked at secondary, if at all. So, if getting a room when you arrive or shortly after is more important, do online check-in. If you'd rather wait for your room type, do normal check-in.
Also, I believe computers roll over to the next day at 7am so that would be the earliest you could check-in.