My concerns would be the tilting or flexing of the wall since the top is not attached to anything. Particularly if the counter top is very wide. The joint I would be most concerned with would be the joint between the studs and the bottom plate.
My approach to to constructing this wall would be to first build a box of the top and bottom plates and the two end studs. Temporarily sit this wall in place and sit my cabinets in place. Mark the location for the internal studs such that they align with the sides of the cabinets. Remove the wall and install the internal studs. Normally you would space the studs on 16" centers to align with breaks in the sheet goods but in this case you want them to be located so you can later attach the sides of the cabinets to them. Because of their better gripping power use screws instead of nails to build the wall. I would also install T straps at the joint between each stud and the bottom plate on the cabinet side of the wall. I would use 1/2" plywood on the cabinet side of the wall up to just below the cabinet counter top highth. Use drywall above that. This would increase the strength of the stud and bottom plate joint and prevent any racking of the wall. I would then install the wall, anchoring it to the floor with screws or bolts. Sit the cabinets in place and attach the sides of the cabinets to the studs using straps or mending plates. You want attach the sides of the cabinets, not the backs to the wall for the greatest strength. The cabinets will will in effect be holding the wall up and preventing it from tilting. Remove the toe kick plates of the cabinets and attach sides of the cabinets to the floor using L brackets. With the wall and the cabinets tie together like this, the wall is not 4" thick, it is 28" thick. Now install the drywall on the other side of the wall.
On the top of the wall install 3/4" plywood, 2" less in width than the counter top. This should not be one long piece of plywood the length of the wall, but should be at least 3 pieces with a 1/4" gap between them. Wood moves with changes in humidity, Corain moves with changes in temperature. Usually these are in opposition with each other. Corian counter tops are usually 3/4" thick with an edging strip added to the underside to give the appearance of 1 1/2" thickness. Use construction adhesive and screws to attach the plywood to the top plate of the wall, screwing on the outer edges of the top plate. The Corian will rest on the plywood and be attached with spots or beads of a flexible adhesive to allow it to expand and contract.
Just my way, but then I can turn any 3 hour task into a 3 day job.
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