In theory, you have a better chance of getting a request met earlier in the day. Rooms are pre-assigned, but they're not actually assigned until you are standing at the check-in desk.
So if you arrive in the morning and learn that you weren't pre-assigned a room that matches your request, you can ask nicely if your request can be granted. In such a case, let's say there aren't any such rooms available in the open inventory, but there is such a room that was pre-assigned to someone who hasn't shown up yet. They can make that room your room, and the person it was pre-assigned to no longer has that room set aside for them.
So, in theory at least, the earlier the better.
But that's just theory. From my last 2 stays, I can give you opposite examples which support and don't support that theory.
I checked-in at Polynesian at 9:45 a.m. I reserved a theme park view room. I requested a specifc floor of a specific building. I was willing to accept anything except one specific floor of another specific building (that floor doesn't have balconies and the view is only so-so). Well, as luck would have it, I got stuck with the one location I really wanted to avoid. So I nicely asked if I could get my request met. The CM did some wrangling and re-assigned me a room exactly where I wanted, with the understanding that my pre-assigned room happened to be available right then but the more desirable room wouldn't be available until after 3 p.m. Fair trade as far as I'm concerned. But keep in mind that I poached that desirable room from someone else who'd already had it pre-assigned to them, it's just that I got there first.
But then there was my experience last month at Contemporary. We were staying using a ridicuously low conference rate (I'm talking less than half the price of the rack rate ... MUCH less). With a conference, at least at that resort, you don't book a specific room type, you can't, you just get "run of the house." Well, at Contemporary, that usually means a room in the garden wing, which is much less expensive than a room in the tower and in my opinion is much less desirable than a room in the tower. I put in a request for tower - theme park view, since I figured it couldn't hurt to try. We arrived around 10:10 p.m., and at check-in I was delighted to learn that we got a free upgrade and were pre-assigned a room in the tower, a tower - Bay Lake view room. WOW! We checked-in after 10 p.m. and yet got a free upgrade to a much more desirable room.
So you never know!