A lot of questions have been asked on stackoverflow that get closed for being offtopic. Some of them have a stackexchange site to be asked today (e.g. programmers, computer science, superuser, serverfault, etc). I'm sure this happens with the "civilian" themed sites as well, but I expect this happens in the computer orientated ones to because they are closely related.
There are probably many good off-topic questions that now have a SE site. Some people might be motivated to actively look for them if such an act were gamified. I think thee badges should be awarded on the target site, and their should be a bronze, silver and gold one. The bronze should be for one question, silver for five, and gold for 10 badges.