Larger jets made a Forrestal-scale carrier likely

Would the Forrestal class still have been built without the Korean War?

Yes. Increasing jet-aircraft size would still have driven the United States toward a larger carrier.

The United States would still have reason to build the Forrestal class without the Korean War because jet aircraft were increasing in size. Larger aircraft drive requirements for deck area, handling space, and a carrier capable of operating them. That long-term design pressure did not depend on one war's immediate procurement stimulus.