Allied surface ships pursue a crippled Japanese fleet

If Allied air strikes remove Japanese carrier aviation, do the battleships and cruisers finish the action?

Potentially; the Japanese would probably withdraw rather than accept the surface fight, exposing themselves to Allied submarines.

American heavy cruisers, British heavy cruisers, and fast capital ships would all seek to close on damaged Japanese ships. Even four Kongō-class ships would face an unattractive surface fight after their carrier cover had been lost or crippled. The Japanese commander would therefore have strong reason to disengage rather than contest a gunnery action on worsening terms. Withdrawal would then carry the surviving ships through waters crowded with Allied submarines.