There will still be an application for open beta, but of course those already in the beta will be given the appropriate key. As for how extensive the application process will be, who knows. I'm just hoping it's enough so I can get in and give it a go, since I didn't manage to get selected for the closed beta period. :)
So far, just have to keep watching for more info on open beta from SE. Start is 2am GMT on Wednesday (7pm PT, 10pm ET on Tuesday), so presumably they'll have to open up apps Monday-ish to get whatever pool they'll be selecting from before the period opens, but that's just speculation on my part.
FFXI: Triane [Caitsith], Retired DRK75, THF75, RDM71
FFXIV: Triane Rhiga
[Besaid] Pugilist, Marauder, Fisher