First and foremost GroupJive is not ACL. It has no control outside of it self. Your users are not meant to have site wide control based off GroupJive. It's for user community groups similar to Facebook and other social site Group usages.
With that said yes it's possible. You'll need to use CB Auto Actions and act on the after join group trigger in a Usergroup action to give them a Joomla usergroup.
My hope is to allow GroupJive group members to have access to certain moderator privileges within other areas of the site.
For a user to have moderator privileges in a group just promote them to a moderator from the Users tab of your group. You do not need or I should say should not give them site wide moderator privileges based off their GJ group.