Am I able to give our support user access to add users to an EAC configuration without giving them full admin permission?

You should give manager users permission if you are plan is only allow them to have user configuration done. 

Delegated administrators can:

• Create and edit users in specified roles and all subordinate roles. User editing tasks include resetting passwords, setting quotas, creating default opportunity teams, and creating personal groups for those users.
• Unlock users.
• Assign users to specified profiles.
• Assign or remove permission sets for users in their delegated groups.
• Create public groups and manage membership in specified public groups.
• Log in as a user who has granted login access to the administrator.
• Manage custom objects and customize nearly every aspect of a custom object. However, a delegated admin can’t create or modify relationships on the object or set org-wide sharing defaults.
• Administer users across all delegated groups to which the delegated admin is assigned. For example, Sam Smith is specified as a delegated administrator in two delegated groups, Group A and Group B. Sam can assign a permission set or public group from Group A to users in Group B.