Maybe this is a dumb question but:
I have a Linux box at home, can I run a GE:S server on my Linux box but play GE:S with my Windows 7 machine on the server with only one steam account?
Running a server WHILE playing GES on it, is just isn't a good idea.
You want the server to be separately running from the client. I used to run a CS Source server and play on it at the same time, and my clients noticed lag as well as the cpu spiked occasionally.
Give it a try though. Make sure you have a good specs to run a good server. Also, dont forget to have good upload bandwidth too.