Delta, like Tom wrote, you could have but, there is a lot of buts… You can have an incompatibility or even do not have some files to be scanned because system mess the drivers it should load to scan a file. For instance, in the past, NAV (only on-demand) prevents avast to scan exe files under DOS). Take care, you never know.
About what Tom posted, you can have avast doing the same - and better - as AVG:
Boot time scanning (or even only memory and startup itens)
Scanning on-demand
Scan downloads (C:\Program Files\Alwil Software\Avast4\ashQuick.exe)