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Yes, you can continue to play games in the archive, but I don't think they will show up as a "waiting game".the archive is a place to save your games. Normally people just put their finished games there. You can put active games there if you want (i.e. opponent quit moving and it has a very long time out). You just have to remember to go back and check on those games.
Archived games remain public.
The acrchive simply prevents having several hundred games on 'my games' page.