Yes, 'done' can have this meaning. But it's rare by itself. You'd more likely see, "A common-law marriage wasn't the done thing in the past"; "Common-law marriages just weren't done in the past."
As Raymott said "... is not the done thing" is the usual style. You might hear "It's just not done" too but context would dictate whether that meant "socially unacceptable" or simply "it doesn't happen".