While I don’t think that avast! GUI will really add much to the resource “load”, and while I am really not sure about the exact setup (whether the service is running or not) - avast! UI process shouldn’t be needed for a scheduled task to run (because scheduled tasks run even if nobody is logged on).
Sure, you’ll need the GUI to create/schedule the task, and you’ll have to stick to the report files (without the GUI process to show the results), but the scan itself should run.