The bypass valve is controlled by the ECU. You should be able to measure the change in vacuum as the step motor is adjusted by the ECU to let more or less air bypass the throttle body. I don't have experience with this particular setup, but typically I would put a T in the vacuum line and hook up the vacuum meter and monitor. If the vacuum drops, more air is being let in, and vice-versa.
What I would look for is if any air is being let through the valve. If the valve is closed, then no air to control the idle is being let through.
For cold starts, the pintal in the valve should be open to allow the ECM to provide a rich mixture and higher idle for cold starting/running. Then the valve should slowly move to restrict the idle air as the engine idle returns to normal. If the valve stays closed at start or when running, then the ECM can't control the idle speed. You can use a hand vacuum pump to check if the valve is closed.
Disconnecting the 'map' sensor vacuum line can introduce additional air to the engine allowing it to idle (and likely run lean, which explains the high exhaust temps witnessed).
I would expect the valve to provide confirmation to the ECM that the step motor has responded to commands, and trigger a code if it didn't, but I don't know enough about this particular arrangement to know for sure.
You can also bench test step motors by applying voltage to the open/close harness pins, and monitor the results on the sensor pin, but you have to know the pinout for the valve to do that.