The closed Alpha stage for Warlords of Draenor seems to be over since Beta stage will start in less than 1 hour (23:00 EU servers time). The confirmation came from this page and from the emails that some of the players received with the first wave of the Beta Invites.
For the moment the test realms are up and they were up for the last few hours but other than the character creations there is nothing you can do to reach Draenor.
By the look of the test realms people are already gathering and prepare to head to Draenor. Let’s hope everything will start on schedule and realms will hold all the players. This is how Stormwind looks like now on the test realms:
If everything goes well for us (EU tests are working strange) we’ll see each other on twitch.