How to replace drywall adjacent to wall cabinets and then tile over it?

I just had the cabinets and countertops in my kitchen replaced. The new stuff doesn't quite line up with the old tile. The drywall behind it is pretty old and torn up, and the gaps between the tile and countertops/cabinet are only about 1", so I'm planning on tearing it out, putting in new drywall, and tiling over it.

Below is a picture of my microwave and a box of Cheerios — and the wall/countertops/cabinets. 🙂

My question is: is it OK to leave a small seam in the drywall right where the cabinet/countertops meet the wall? I don't see how I can mud over the seam since it means I would need to mud under the cabinets/countertops. Can I just caulk the seam, or will the tile grout be sufficient?

Thank you!