Lately my room ready texts have been coming around 3-4 pm. Before your arrival is possible but it is not guaranteed. You can designate early arrival, but you have to acknowledge that it's a priority over any of your other requests.
It doesn't really depend on time of year. It will depend on when your room is actually designated as ready. Which has to do with things like housekeeping schedules, and when the previous guests vacated.
If you've done the online check-in, whether the room is ready upon arrival or not, you can bypass the desk (if the system works correctly and you get the ready text). But if the room isn't ready, you'll need to go someplace else first. If you didn't get the ready text by the time you arrive, and you want them to try and find you a room that IS ready for occupancy, you'll need to go to the desk.