It might work.
They work with rear-projection screens as long as it refreshes well below 100hz. Might work with a straight projector.
Light guns work by detecting the nanosecond flicker on the screen as it refreshes.
They don't work on LCD screens because they don't have an off state in their refresh.
To assure it works, you need a CRT.
Or limit yourself to Wii-style shooting systems.