A stern Icarus installation was possible but costly

Could a County-class destroyer be rebuilt with a stern flight deck and Icarus installed aft?

Yes in principle, but making the full arrangement work would require considerable engineering.

There is no fundamental reason an Icarus installation could not be placed at the stern. The difficulty lies in integrating the proposed flight deck, missile, and antisubmarine changes into the existing hull. None of the individual ideas makes the conversion physically impossible. Making the complete arrangement work would still require extensive redesign.