How did you back up your site? Did you just use the Export option in WordPress? That does not export any data from plugins that use custom tables for data such as Connections. If you didn’t delete the database from your other WP installation, no, you data is not lost. You can use a tool such as phpMyAdmin and export the Connections tables from the database an import them into the new database. Another solution … if the old site is still accessible you can use most of any of the WordPress Backup plugins that are available as most will backup all custom plugin tables too.
I hope that helps!