I'm sure you noticed, when putting them in enclosed on 2 sides, that it's never a perfect fit? Just the thickness of the DW tape in the corner guarantees it, never mind a slight warp in the studs, or being a tiny bit off on the layout, so it's no quite exactly 90 degrees?
I've done it with laminate tops, where I was able to scribe the counter to the wall. Can't imagine doing it with a top that can't easily be cut onsite...
Maybe drywall only the bottom of the walls, then install the counter, then DW above? That extra inch would make life it a lot easier.
I dunno, but it sounds like that'd look...weird... compared to the original layout with it at the back of the 4x4 space. All the walls are already framed? Already rocked & taped?
I suppose another way, would be to cut out just a section of the DW, to make the install easier, then patch...