Short version: Don't do it. Let them signup for GOG.com and buy their own.
Let this be a lesson that they should backup their games or take better care of them. I recommend backing up every new game you get and only using the backup for installation, playing, etc. :)
That's part of the issue though. Due to the copy protection on a lot of games, making legitimate backups is quite nearly impossible without taking the risk of downloading some crack of a very disreputable site.
I'd have to say no but only just. If it was just the licence for the game then that'd be okay in my book but part of what we pay for is the compatibility work done by the GOG team so there's no pissing about getting the game to run.
If it's a game like UT2004, for example, which seems to contain nothing GOG-related, aside from the installer?