When a RDP sessions time out, what happens to the running processes? Are they gracefully shutdown, and if that fails then forcefully terminated?
It depends on the settings on the Terminal Server. Specfically the Session settings for RDP connections. Provided you have appropriate permissions to access them, they can be accessed via
Administrative Tools > Terminal Services Configuration > Connections
You can configure it to end disconnected sessions immediately, or after a certain time, or never.
Have a read here http://technet.microsoft.com/en-us/library/cc779468(WS.10).aspx
If the session is configured to end, the result will essentially be the same as logging out.