Some property management systems (PMS) can be integrated to these buttons. It is certainly an option, but you wouldn't find most small hotels to PAY for all that, as it can be very expensive and would need to tie into a BacNET system to facilitate, usually through a connection to an Inncom thermostat. Large hotels can and do drive efficiencies through these.
Large hotels have also moved away from clipboards of room information and utilize systems like HotSOS and REX to the PMS system when the room has been clean and is ready, or if the guest has a DND on their door, keeping things real-time.
As far as when your room is cleaned, it generally goes in this order:
1. Cleaning rooms to accommodate guest arrivals.
2. Cleaning rooms for guests staying over night.
3. Cleaning rooms that have been checked out and are not expected to be needed that day.
HotSOS/REX provides an order of rooms for housekeeping to be assigned to, in a specific order for more efficiencies.
If you expect you may be back before housekeeping finishes your room, the simple answer is to stop by the front desk and request your room be cleaned early. When using HotSOS/REX, they can be queued to the front of the list. Without such a system, it can be communicated to the staff by printed sheets, radio, daily standup meetings, etc.
Now when it comes to your average 100 room hotel, most likely none of this is happening. Large hotels, especially Vegas and convention hotels, certainly do this.
I am hospitality systems manager for an 800 room corporate training center and hotel.