The only "test" is to unplug it. If there's no change in the idle performance, then change it. They can be cleaned once or twice, but this is a temporary fix. I would try the battery disconnect/idle re-learn trick first. https://www.muscularmustangs.com/idlereset.php
No. the idle will have a constant 100rpm up and down surge with the a/c on. If I turn it off it will sit there and idle steady. At times my rpm's will go crazy jumping up to 2000 or so and hunting. I can usually turn the car off and restart it and it will level back out.