I'm not sure if there is a deadline to the US one... the Japanese one had a deadline of August 11th
to download the theme in order to be qualified for a potential invitation (but it also started before the US one).
I don't see any expiry notice on their announcement (below) though, so maybe there isn't one for the US one http://blog.us.playstation.com/2008/...-how-to-apply/
Also, I imagine you will have to be logged into your PSN account and download the US PS Home Theme
so they know who you are.
While you can grab it from the PS3 Themes Forum to install, how would they know who did it unless it tells them the next time you go online etc.
I don't go online with my PS3 at all, so if someone who got accepted or knows more can reply to clarify that would be appreciated.