If you're using v4.3.x on your Joomla 1.5 website, you can do exactly what you stated. The table structure is identical between v4.3 and v5.0, so copying the tables from the old site to the new site will simply copy all settings, user connections, and everything else JFBConnect stores to the new site.
If you run into any issues or have any questions, just let us know. We anticipated a lot of users upgrading from 4.3 to 5.x and intentionally kept the tables the same to make that process as easy as possible.
Best of luck,
Alex
Migration info
