At first glance I imaging it would work out just fine. The question would be if steam would match linux and windows users or a custom sessions setup would need to be used.
Previously I have had a dedicated linux server that worked connecting both windows and linux machines. I have also successfully used a listen server for windows to windows.
I’m guessing in this case having a dedicated server just for match making would be ideal to bring together different OSs and different platforms. I just thought I would see what others thought or had experience with before starting to design and test for this.