I didn't have an issue when I ordered at 4:30am EDT. I know way early, but I woke up for some other reason so I punched it in really quick and went back to bed. I just tried to check on my order and no go. My guess is that everyone is up and pounding the servers.
It seems like it does, I've been checking the premier site since 4am EST and it wasn't until 9:30est that they updated the site and was able to pre-order the iPhone 4