Wow, that's a good idea.
Use case: Today a client asked me to make a change to a live website. I opened the relevant files on my local copy of the website, tried a few things, figured out the best way to implement the change, opened the versions of the same files on the server, and copied various blobs of text from one to the other.
(As I type this, I am aware that it's not the most awesomely rigorous process, but I think most of us live on the edge sometimes, right?)
Anyway, you can see how a quick visual cue as to whether I'm in the local or the remote version of a file would be helpful during this process.