Anything is possible. Your mileage may vary. But if you want to go by statistics, the later you arrive the less chance you have of getting your requests granted.
Yes, rooms are pre-assigned, but ALL rooms that haven't been checked-into yet are free game for cast members to give out. I've had it both ways ... I've arrived early and claimed someone else's room, and I've arrived late and received a hugely surprising free upgrade.
Polynesian, around 9:30 a.m.: I paid for a theme park view. I put in a request for 3rd floor Tahiti (bigger rooms than the other two theme park view room buildings, not all rooms in the other two buildings have a balcony, and one of those other buildings has [in my opinion] pretty stinky views). Well, it turns out I was pre-assigned my very least desirable room (stinky view, no balcony). I asked nicely if I could have my original request granted; the CM got on the phone with Mousekeeping and eventually told me I could get what I want but the room wouldn't be ready until around 3 p.m. (it turned out to be around 5:30 p.m. or so). The resort was sold out. The only way I was able to get what I want is they took that already pre-assigned room from someone else, someone who hadn't checked-in yet, and they gave it to me. Had I arrived 12 hours later, chances are those "good" rooms would've been gone already, whether by people who had them pre-assigned and/or by people like me who requested a change.
Contemporary, around 10 p.m.: We paid a ridiculously low conference rate (about one-third of the normal rate), and as part of the conference rate we weren't able to book any specific room category, we would just get what they call "run of the house," meaning we just get whatever is around. I put in a request for tower - theme park view because I figured why not, what could it hurt to ask for the best. But I was totally expecting a garden wing standard view, not only because of the low rate but because of my late arrival. Well, imagine my happy shock just after 10 p.m. when the CM told me we had been upgraded to a tower - Bay Lake view. WOW!
So I've had it both ways ... I arrived early and snagged a good room only because I arrived early, and I arrived late and got a dream upgrade.