Should avast be listed in the exceptions tab? If so should it be checked or unchecked?
It depends on two things, what version of Windows are you using ?
If XP, then it isn't necessary.
If you are using Vista and you have enabled outbound protection then Yes, if the outbound protection isn't enabled, No (recommended, but it isn't very friendly).
The three avast processes that require internet connections are avast.setup (the update process), ashWebSv.exe (the Web Shield) and ashMaiSv.exe (the Internet Mail provider, if you are using pop3 email).
The main issue is are you having any problems as scythe944 mentioned and if so what ?