No, it wouldn't. Kids who stay in school tend to ingest less narcotics than those who drop out, so therefore, School would be a prohibitor.
I don't think there should be any question that video game players do indeed do more drugs; several studies have noted this, and one did so quite recently. The question left, of course, is whether this is a correlative or affecting relationship, and it seems much more likely that it is correlative. Which is to say, games aren't causing people to do drugs, it's just that drug users tend to be the type of people who also like video games.
That's still not flattering for video games, but it's not nearly as dire as Thompson or other activist groups might claim.