Drush over local network share?
In theory yes. Windows is a bit more difficult because, windows. 

But if you have Drush installed locally, and it's the same PHP version as you have on the server machine it should work. You will need to modify your DB credentials to reference your database by network accessible hostname or IP so that your machine can connect to the database on the server remotely.

Disclaimer: I've never tried this, but it should work. YMMV etc. 

The more "right" way to do this would be to set up an ssh server on the windows box server, and set up Drush aliases to act against the remote server with Drush installed locally on the server and client. 

I don't know how well that works on Windows but quick reading suggests it should be possible.