Yes, once you have set up your conference on ClassTag and have parents invited to your class, you can click on any empty slot and assign parents to it.
Click on 'Choose timeslot' or 'Show more' and all the schedule will open up.
Select the slot or request you would like to assign the parent to.
Select the parent to assign from the list.
Please note: Parents can only assign family members to requests, but not other families.