Should work but keep two things in mind:
- The area outside of the monitor has to be covered from behind with something dark or you will be able to see through it, if there’s even a little bit of light behind it.
- The screen’s shape itself might still be visible because, unless you have an expensive LED screen where black means black, since there will always be some backlighting or clouding.
A good screen might have a good enough contrast so that you could use some tinted wrap on the whole backside of the mirror (or just on the screen) to counter that backlighting.