The Ki 84 Hayate was a very good Japanese fighter. Although plagued by poor workmanship due to the war situation in Japan it could definitely hold its own against the best US fighters of the late war period.
Out accelerate? Possibly but usually not. The Hayate's engine had serious problems developing full power for a large number of reasons including:
Poor fuel pump pressure development and inconsistant fuel delivery.
Cracking of the exhaust manifold
Cylinder head failures and cracking

Climb? The Ki 84 outclimbs late model P-47s slightly. It is about equal to the P-51.

Break off combat? Not likely. Under most conditions the Ki 84 is anywhere up to 50 knots slower than late war US fighters. It also has less range. High altitude performance in particular suffers, particularly above 25,000 feet. This last problem is endemic of Japanese aircraft due to lack of good turbo / super-charging systems.
Against USN aircraft the Ki 84 might have more of a chance to break contact.
Personally, I think that Kawanishi's N1K2-J Shiden Kai fighter is better. In one rather spectacular dogfight one of these fighters flown by Warrant Officer Kinsuke Muto of the 343rd kokutai took on tweleve (12) F6F Hellcats shooting down 4 and fighting the rest to a draw forcing them to break contact. Like the Ki 84 the N1K2 suffered a big performance drop above 25,000 feet or so.