"No icons on the desktop" doesn't sound as a "real" Avast issue. If all those icons were infected programs, for example, then it might be a possibility. But I doubt each and every icon on your desktop is an infected program. You probably had shortcuts, just as the shortcuts of the start menu.
So either you are seeing something else (like some "sandbox / safezone" or alike), or your system has changed for some reason (like screen resolution, but I also doubt it's *that* simple), or you were really infected and what you see is some strange consequence (or maybe something else is going on but I am not thinking about it).
About your question, files can be re-scanned in the chest (without having to restore them). Leave them there for now (safest option).
Could you provide some more specific info? OS? SP? x32/x64? Avast version and edition? The list of files and the original locations that are being listed in Avast's chest? Is your system booting correctly? Could you try rebooting and checking if the behaviour is repeated?...