How Yamato intelligence might have changed British construction

Would the Royal Navy have believed plans showing that Japan was building Yamato?

Yes. Earlier knowledge of Yamato's armament might also have prevented the suspension of some British capital-ship construction in 1939.

The Royal Navy would have believed reliable plans showing that Japan was building Yamato. Knowledge of its 18-inch guns would have made the implications more pressing. In this counterfactual, British battleship and aircraft-carrier construction might have continued through the changes of priority in 1939. Escort production would still have expanded, but the pause in capital-ship work might have been avoided.