Looking at the current login screen, the current server is running Exchange 2010.
The screen shots you have posted, the login screen for the web interface in these is exchange 2007, so you can see the difference.
So it should work fine with mail since the backend is not Exchange 2003 or earlier.
But it's running 2010 behind Forefront TMG, so it's potentially not going to talk through. Depends on what they have set up in TMG. I don't run TMG, but I run a 2010/365 Hybrid Coex and for mine you have to be on VPN to hit the internal server with a client, or go through OWA. He could have something similar.