This article is spot on. An excellent description of the way traffic flows through airspace and the role of ATC in movement of aircraft. I can add that as a pilot is would be a bit disconcerting and unusual to be on an instrument approach into an airport and be handed off to the tower only to receive no response. This would likely happen with only a couple of minutes of the flight left and at a time when workload is high (assuming IMC conditions). There would probably be a little confusion before deciding to switch back to the previous frequency.

Not particularly dangerous - but the pilot does have to be prepared for handling some atypical tasks on an otherwise routine approach

Edit to note: VFR (visual flight - night or day) would be a non-event (from the pilot's perspective) with a sleeping controller so long as traffic is relatively light, as it would be at night most places