Realistically, even leaving the key on isn't a complete test, it only confirms the oil pressure switch and buzzer are working. The trans and coolant overtemp switches don't get tested.
Correct, all that's being tested is the actual annunciator and circuit via the low oil pressure switch, which is closed at rest. I routinely encounter alarms that are inoperative, usually the result of wiring issues to the annunciator or oil pressure sender, and rarely an oil pressure switch itself.