Yes, Jury duty has nothing to do with your current employment status. If you are a registered voter you will more than likely be called for Jury duty and you must attend or have an legitmate reason why you cannot attend.
I think your pretty much okay jury duty i think you just have to let unemployment know you have been summons for jury duty also let them know if you actually do it or not that way they know what your doing you might still have to do your work searches.