I am working on a wall that will separate the main basement area from the storage area (with a door). This new wall will run along the above floor joist which removes the possibility for drywall anchors. I cannot add blocking there either because it is covered for an air return from the main floor.
The attached image shows a basic view of the proposed wall and where it would run along the joist.
Can I still put drywall up without anchoring this edge? Will the wall's future drywall butting up against the loose ceiling edge be sufficient to anchor it?