Early Access ended Thursday, August 29th at 11:59 PM.
There isn't any reason the servers would clear up because no one is leaving. There may be a few people who haven't received their physical copies to register them, but the number of people with this issue isn't large enough to make an impact. Early Access was only available through pre-order. Anyone who bought the game this way also received a 30 day trial which started on the 27th and is going to be extended anyway due to all of the server congestion.
Well, it was also available if you were a legacy account holder.
I've registered zilch codes since I got my original alpha and beta codes and I played right on through Early Access without any issues. I'm wondering if SE sent me some new code for 2.0 or they just rolled my SE account on up without any effort on my part.
I guess I'll find out this afternoon when I try to log in!