No, I don't think you'll need to override all the coding.. thankfully. Though, there may have to be some changes to code somewhere.
The "Register" button on the SCLogin module simply brings the user to the standard Joomla Registration page. JFBConnect will automatically add the social login buttons to that page. Some extensions have a system plugin which is meant to redirect any requests to the standard Joomla registration page to their own registration page. From your description above, Jombri sounds like it's performing such a redirection.
That's actually ok. You'll need to add the JFBConnect social login buttons to the Jombri registration layout page, which we try to make as simple as possible. I can't tell you the specific template file to edit, you'd need to contact Jombri or consult their documentation. Once you know the right file though, all you have to do is add the following 'tag' to the page:
JFBConnect will detect and replace that tag with the proper social authentication buttons that you've configured. There's lots of parameters you can also configure in that tag for which providers to show, which image to use and other things.. but for now, get started with that tag. Once the social login buttons appear, you should be good to go.
I hope that helps explain, but if not, let me know and we'll help however we can.
Thanks,
Alex