This is somewhat exciting, but less so than a Beta Weekend with the EU included. See, general game testing seems to include a whole lot less people, thus your chance to get in is much better on a Beta Weekend. This is of course tempered with the fact that a general beta invite means you get to play for more than just one weekend.
General Game Testing Invites are now being sent to EU testers.source
Sent Nov. 10: General Game Testing Invites
Who was invited: Testers from all European launch countries (see list here)
What was sent: General Game Testing Invites
Server locations: EU servers
Invite status: Invites will continue to be sent during today. E-mails can take some time to be sent, so please check your www.swtor.com/tester page to be sure!
Personally I am hitting F5 on the swtor.com/tester page right now.