Hello Chris,
I am really sorry for the delay of this reply as it is a weekend for us here. It's currently not possible out of the box but if you add the block of codes below in the file /components/com_easysocial/controllers/notifications.php at line 241, you should be able to mark them all as read when they click on the notification icon,
$model = FD::model('Notifications');
$state = $model->setAllState(SOCIAL_NOTIFICATION_STATE_READ);