Does g dragon have a Facebook?

Yes, he doesn't have a personal one but there is a professional one made by YG Entertainment. It's facebook.com/gdragon

Just for future reference, ANY K-Pop idol is 99% NOT going to have a personal facebook account. Why? Because for one, it'd be too risky and their company wouldn't let them, and two, facebook just isn't that popular in South Korea as some may believe. If anything, they'd have a me2day which is the equivalence of a twitter.