Assuming the NDA even allows you to say that you're in, I'd say 25 seconds after someone gets their confirmation Email

This is true.
As I recall, Dragonborn beta testers weren't even allowed to mention they were in the beta.
edit: Makes sense. Someone who reveals they are in the beta. Even if they don't post any details, could trigger a load of posts begging for details or even make someone else in the beta think it's okay to post stuff as 'it's the official forums'
I do agree with the need for an NDA especially during the early beta stages. We saw what happened on the Dragonborn forums where people saw Reikling Spears and the character on a dragon. and whipped it up into useable spear weapons and free roam dragon riding. And that was just in the trailer.
With a beta it'd be worse. Someone posts about a feature that is later removed or disabled. Game is released, people are ranting because they'd read about this feature and was looking forward to it and now it's not even there.