I just applied the code (I assumed it would do it automatically) and purchased some game time, but I still get the error.
I see an official response on the forums:
https://forums.wildstar-online.com/forums/index.php?/topic/55715-headstart-issues-31514/
Some users are reporting they are being bounced between NA and EU, receiving a "No Valid Game Account" message.
POSSIBLE FIX: If you have only just activated a pre-order code/recently applied a code, you may need to wait 1-2 hours before the system registers your account correctly. Wait 2 hours and try again.
Edit:
Update-
Some users are reporting they are being bounced between NA and EU, receiving a "No Valid Game Account" message.
Update: We're still investigating the issue with "No Valid Game Account".
We will try and update you with information as we receive it, but there are a lot of moving parts right now and we're trying to get everything up and running so please bare with us! We're working on these issues as fast as possible and are sincerely sorry if you're unable to get in and enjoy WildStar right now.