This is a great question. Similarly, I had wondered whether it would work if monitor is not an apple monitor. In order to test this I disconnected my Mac Mini from my Mac Thunderbolt Display and covered up the monitor so that it wouldn't be seen by Apple Vision Pro. I found that I was still able to connect to the Mac mini. The quality of the image when connecting to Mac is fantastic. It works very nicely as an alternative display. I love that I can easily reposition that virtual display anywhere I like and can change its size at will.
That said, I don't think I could use the Apple Vision Pro for as much time as I use my regular display each day, so I would still recommend having a monitor. Depending on your application you might be able to get away with spending less on the monitor than you would have otherwise.