You should be able to to deploy to all machines, and it should work with UNCs as far as I know.

However, the way it runs now, it would overwrite the log file every time it was run from a client. There are a couple options to get around that. Use an INI file instead of a txt file and create a new section in the INI for every workstation that it runs from. Or you could create a different txt file for each machine that it runs from.