Well, yes...however I think some people would have an issue with their DOB being collected. Some people already don't like that IRC networks collect email addresses and store them. The more personal information you collect, the more liability you have. I've seen COPPA issues come up on IRC before - so while it's a good idea in theory it'd be hard to implement.
I think if someone were to do this, it'd be easier to collect by age. Instead of getting a DOB, users could be prompted for their age. Services could then "forget" this information after it was checked. This means it would have to be entered every time they wanted to come in the room, but it'd be less personal information to collect. Again, this method would be easy to fake though. Hard to say.