Should I cut back drywall before installing a new wall?
Normally it's not necessary to remove drywall when adding new walls. You'd just install studs tight to the existing drywall and nail or screw through. For the ceiling, cut openings to add backing if the plate is parallel to and between joists, otherwise just fasten to the joists through the drywall.
An exception might be where you lack midpoint backing and want the studs mounted securely for reasons such as door openings right at the end. If you don't have backing you can use construction adhesive or toggle bolts to secure the middle of the stud, or just rely on the top and bottom connections and the tension of the drywall on the new wall.
So, no.