Yes. Please retrieve the following configuration file from your backup:
Little Snitch 6
/Library/Application Support/Objective Development/Little Snitch/configuration6.xpl
Little Snitch 5
/Library/Application Support/Objective Development/Little Snitch/configuration5.xpl
Little Snitch 4
/Library/Application Support/Objective Development/Little Snitch/configuration.xpl
You can then restore your rules from that file via Little Snitch > File > Restore from Backup (in case of Little Snitch 4: Little Snitch Configuration > File > Restore from Backup).