Within the past few months I conducted such a test. Well, actually my goal was exit row seating, although I think that's a distinction without a difference for these purposes.

I tried checking in online at 36 hours out and at other significant times (e.g., 24 hours out and 12:00 midnight on the day of the flight). I even drove out to the airport and tried using the self-service kiosk four hours before the flight. The test confirmed that non-elites can't snag an exit row seat until two hours before their first flight.