If the version is 8.0 and above then yes, it runs all the time.

Every time you or a program tries to access an infectable file, avg silently scans it. AVG refers to this as the resident shield. 

• If you get your e-mail with a Outlook Express or a similar program that uses POP, AVG's E-mail Scanning will intervene and scan the messages. 
• If you have the Linkscanner enabled, google and maybe some other searches will be screened for known sites that contain viruses. 
• If you want AVG to scan all your files, however, a system scan must be performed, which can be manually started or scheduled.