Test if webcam picks up infrared
There is no way in software to determine if a webcam is sensitive to infrared, unless you have a separate computer controlled IR emitter which is visible to the camera.

The aspects of a webcam that determine it's infrared sensitivity are both hardware, and non-electronic, which renders them completely invisible from the computers perspective.

The only exception I can think of to this is a webcam which specifically advertises itself as being IR sensitive, in which case you could do an online lookup based off the VID and PID to find the model, and look at it's specifications.

To be specific, the optical component responsible for blocking IR is a hot mirror.

Fortunately, removing the hot mirror is very easy, and there are many, many, many, many walkthroughs.