..."can having many disconnected sessions cause a performance issue?"
When you say "many" you can only have a max of 3 remote, interactive sessions (including the console session) on a regular 2008 server (terminal server not included) so we are not talking about a large quantity of sessions. Even so...
"Do the disconnected session tie up any server resources?"
Yes. Anywhere in the range of hardly any resources to almost all of them if the user kicked off a process that uses a lot of CPU and RAM. You should have a resource monitoring system in place to determine resource usage on your servers in general.
In practice, disconnected RDP sessions are not typically a concern (except when you are trying to RDP in and can't because all the remote sessions are in use already...) although it is probably a good practice to clean them up every once in a while. I have never experienced any significant issues due to disconnected sessions, but this depends on your environment too. If you have 20 admins all logging in to your servers and getting disconnected all the time, that could cause issues for other people trying to remote in.
You can control Terminal Services behavior using Group Policy settings - specifically using a combination of the Session Time Limits settings to automatically log off disconnected sessions if they are an issue in your org.