Specifically towards the OP: It depends on how polished the Closed Beta is. Perhaps more to the point, it depends on if the Beta is going to be a true beta, in which case they should be taking it very seriously, secrecy and all, or a glorified demo, in which case, of course they should publicize the hell out of it.

Given FFXIV's global image, about the worst thing they could do right now is have videos of glitchy, unpolished gameplay floating about. On the other hand, if the Beta is merely lacking a few applications of finish, by all means I would imagine a very light NDA if any.

Of course, most people probably don't care for my opinion on the matter. I believe in the return of a strong beta that really tests core mechanics out of house. I think that that should be accomplished by a small, carefully chosen group at first, even if that means me and my fellow Legacy players don't get in on the first wave. But that is a discussion for another time.