If I understand the question, there could be an issue with the wall framing being discontinuous at the top of the block. The required lateral bracing of the exterior walls would be severely compromised. You would probably have to convince a building inspector that reinforcing from the foundation up through the block wall was adequate to brace the wall (if in fact it's even possible which I doubt). Where I live that would require a structural engineer's stamp.
I suspect the only practical alternative would be to add stone veneer on the outside of a full height structural stud wall.