They will hang around for a while. There is a possibility they may serve as laser platforms and drone command and support...
Anything that floats can be detected and sunk with weapons that can be a continent away. Within ten years even the battleship admirals who dutifully patrol the Pentagon and the corridors of Congress will come to this realization. It was 100 years ago that General Billy Mitchell demonstrated that battleships were no match for airpower. Who will be the Billy Mitchell of the 21st century?