I don't think time of day matters but maybe the day of week would make more difference. Once we checked into CB at 10:00 a.m. not expecting to be able to get into our rooms and they were ready.

The only preference we had was a bottom floor room. We not only were given a bottom floor but right in front of the bus stop and next to the food court/pool area. This was a check in during the week.
Another time we checked into POR at 7 a.m. and knew that we would likely not have a room yet, but wanted to get to the park before opening. We had 2 medical requests on our reservation. At check in I specifically asked if we would be close to the main building area (for mil who has difficulty walking) and also ground floor (sil and mil are legally blind) since there were no elevators and stairs were not a good thing for both medical situations. The CM smiled and said that both medical requests were being met and had us park in the parking lot for bldg 14. We weren't able to get into our rooms (not sure why when they say by 3 or 4p.m.) until after 5 p.m. but when we returned we found that not only were we the farthest from the food court but we were also given a top floor room which was not accptable. At this point it was after 5 and we had dinner ressie's at 6:30.
After a lengthy time back at the check-in counter we were finally switched from AB section (because of trundle for one child in each room) to the Magnolia bend section. Bottom floor this time but still quite a distance walk (which we ended up driving mil up to the front each day and parking there).
They even ended up throwing in roll-aways to replace the trundle beds at no cost. Our luggage had also already been delivered to the other room and they had someone help with the move. We barely got moved into our new rooms in time for our dinner ressie. This was on a Sat. check in.
I really think our original room was given away since we were not there when it was ready and they overlooked our medical requests. By the time we realized where we were located the resort was filled up mostly and didn't have many other choices of locations.
We didn't make a big stink over it, we just wanted at least the bottom floor need met because of safety reasons. We still had a great stay and we just now have to go back and try the AB sectoion on another trip. Just means...back to disney!
I don't know if time or day of check-in has anything to do with it. Even request(medical) don't always make a difference. I really think is luck when you get what you want. That being said, we were in Disney...I didn't care where I got to sleep.