The short answer is: No. If you have JIRA and JIRA Service Desk you will only need one license: EasySSO for JIRA.
Your license level is dependent on your JIRA users, Service Desk customers don't need to have a license. Please remember if you have approval processes in your JIRA Service Desk approvers need to be licensed as well.
Happy Service Desking and give us a shout if you have any problems or suggestions.