They won't shut the servers down untill the 2.0 Open-Beta otherwise not everyone will be able to play FFXIV.

1.23 & Closed 2.0 beta's will run side-by-side and 1.23 will be turned off around 2.0 Open-beta.

I don't think they'd be stupid enough to close 1.23 down and 1/2 the playerbase doesn't get into the beta, they risk losing 20k subs or so.