In an attempt to consolidate the FC->FB import discussions, I'll suggest we discuss over here: http://forums.adobe.com/message/2003319
But to briefly address your specific issue here...
I'm guessing that you probably do not want to copy/paste the Catalyst-produced Application directly into your FB project, but instead perhaps:
a) Import the Catalyst FXP as its own project, add your extra FB code to that project.
b) Import the Catalyst FXP as its own project, copy the components from it into your FB project, use them from your FB application.
c) Import the Catalyst FXP as its own project, copy the components from it into a new Library project
d) Import a Catalyst FXPL that consists of the components you created in your Catalyst application. This will allow you to more easily separate your reusable components into their own project in a more automatic fashion.
If it's possible to keep a lot of the functionality out of the Application and instead stuffed into the components themselves, this may help save some time later when continuing development with the code in Flash Builder. Basically, all I mean is that if you create multiple application-level States ("Pages") in Catalyst and then rely a lot on transitions between them, etc., then you'll be more likely to have to factor all that out functionality that's baked into the application when you are working in Builder. For this reason, a more "developer-friendly" Catalyst app may involve a single Catalyst page which then has all the functionality stuffed into the content therein. However, based on your design, this may or may not be practical and you may lose out on some features in Catalyst by limiting yourself to a single page. I'm not a Catalyst pro myself, so I'd suggest you checkout the Catalyst forums to look for further tips.
Developer, Flash Builder