The tray icon isn't the cause of the slowness, the main avast service avastSvc.exe will be running in the background scanning activity. That is what resident, on-access AVs do, so I would follow the suggestion Bob made in Reply #61 check what programs are running on boot.
There are many programs that want to run on boot when there is absolutely no need for them to do so, typical of this are media players when you only need them when you click on a media file. I would probably go further and not just delay them using WinPatrol but decide if they really need to run on boot.