Git works on files. With the way you describe it, you will be running git on your windows pc - the fact the files are actually being accessed via the network rather than directly is something git probably won't even be aware of. As long as that is the only machine accessing that share, it should be fine.
But it's not really how you should use git. It has it's own mechanism for pushing/pulling changes between machines; so unless you are running an interesting driveless setup, you should probably consider storing the working directory on the machine that it is being edited on. Especially if there is a chance the files could be accessed from the linux machine as well (mixing version control accesses to the same working directory between multiple machines is always a bad idea, let alone between multiple OSes.