Your best bet is setting up your own WordPress plugin server and deploying your theme to that — then install the plugin that interacts with that server on all of your sites and hey, presto! You’ve got yourself a custom theme which updates through the native interface!
And you save yourself a whole lotta trouble having a unix folder with multiple users and one file that they all access (which would probably end up with access conflicts etc)…
See WP Update Server on Github to get started.