Redirect to login on form submit
This might help in terms of understanding Rules: https://drupal.org/node/878718

And in terms of flow, I think you could use a rule via the Rules module to direct them to a login page specific to them (people who have just filled out the form), and then the Login Redirect module to redirect them back to the form/submit action after they login. That's assuming the information they entered would remain in the form. You'll probably have to do some experimenting with that. 

Jennifer