Hi Leva!
Thanks for the request -- it provides us a lot of good feedback to hear what others would like to do alongside Eventbrite registration.
Unfortunately, the actual 'registration flow' of Eventbrite is pretty well locked down, so this wouldn't be possible in the way that you've described.
I could imagine an experience where are user comes to your site before Eventbrite, and is initially forced to register or login (if for these events, an account is required). You can manage this by having a private event on Eventbrite, or by using our access codes:
http://developer.eventbrite.com/docs/event-access-codes/
Sorry we don't handle this in an ideal way, if you end up choosing Eventbrite, then we'd be happy to answer any follow-up discussions.
Cheers!
Mitch