You could test this by replacing a steam application with the demo from here, but I somewhat doubt that SRPT goes as far as registering virtual keyboards/mice. A tool that I'm currently developing allows to write input adapters to map keyboards/mice to a virtual gamepad.
I added it as a non steam game to my library. but that does not support remote play together. I also tried through parsec but it just gives remote players control of the host mouse. Would be a huge deal if it did work though.