Heavy-lift ships for damaged warships

Would ships capable of carrying other ships have helped move damaged warships in World War II?

Yes, greatly, but their cost and complexity would reserve them for the most valuable ships and specialist jobs.

A semi-submersible transport can sink down, float a damaged ship aboard, and then raise both hulls for the voyage. Such vessels would have been extraordinarily useful for returning some badly damaged warships to repair yards during the Second World War. They are themselves complex and costly capital assets, however, and cannot be stationed everywhere a casualty might occur. Even in modern service their use is normally reserved for oil rigs, expensive warships, or other specialist loads whose value justifies the operation.