The short answer is: No.
If you have Jira and Jira Service Desk running as one application, you will only need one license: EasySSO for Jira.
Prior to Jira 7, Jira Service Desk was offered as an add-on to Jira.
From Jira 7 onwards your 'Jira Service Desk' is marketed as a standalone application, a construct that bundles Jira Core and service desk functionality, but effectively JSD remains an add-on.
EasySSO for Jira does work with Jira Service Desk.
Happy Service Desking and give us a shout if you have any problems or suggestions.
Please read our FAQ titled: What user level do I need for EasySSO on Jira Service Desk?