If you're only using JFBConnect for user registrations then yes, the user map table is what you need *as long as* the Joomla users from the old site are on the new site as well. The user map table only maps Joomla users to their social network users. If you have not migrated the Joomla users from your old site to your new site, then you wouldn't even need the data from this table.
In general, our DB tables are set up by the configuration settings in the different areas of the backend. Since you're not using the other features such as Open Graph, Channels, or Requests, if you've configured everything in JFBConnect already, then the #__jfbconnect_config table will already have the settings you need. As long as the Joomla users are present on your system, then yes, the user map table should be all you need.
-Melissa
How to import jfbc database tables to new site?
