Yes, you should prime the whole surface.
Sealing/priming helps prevent penetration of vapors and moisture from the air into the drywall. If you don't seal the entire surface, even though it's behind cabinets, penetration can happen - mind you it's not going to be significant but it can happen.
Plus the time involved to paint behind those cabinets that aren't there yet is minuscule.
This is unrelated but I don't understand your painter's objection. Painting a wall with no cabinets on it is orders of magnitude easier than painting a wall with cabinets already mounted. With cabinets in place, you've got to tape edges, you risk getting paint on your new cabinets, you've got a much harder time accessing the exposed wall (cabinets get in the way), and so forth.