Should one insulate rim joists prior to adding drywall if batt insulation already exists?
Short answer: Yes.

What you're missing from the rim joist insulation is vapor barrier.  So you should pull back the the insulation in the ceiling, then either insulate the rim joist with foam (ideally with sprayfoam around board foam so that there is zero air movement against the rim joist) or insulate with batt + vapor barrier.

It's really important that the rim joist has insulation and a vapor barrier, or condensation will form on the rim joist and drip into the ceiling, or cause mold to form.  Over time it could cause joist hangers against the rim joist to rust or the ends of the joists to rot - then it becomes a very complex and expensive to fix.

It is not sufficient to just put vapor barrier on the bottom of the joists, as this allows too much air movement, and that joist space is not vapor tight.