Very unlikely. The F4U and F6F were very much like the P-47, extremely rugged airframes that, quite by accident, turned out to be just about perfect fighter bombers for the era, to the point that both services effectively abandoned dedicated "attack" single engine designs (by mid 1944 the USN was actively retiring SB2C divebombers and converting those squadrons over to F6F, and more rarely F4U, squadrons). The rugged design of the R-2800 and the rest of the airframe allowed the various aircraft to take huge damage and keep flying, making them ideal for the CAS role, something the various liquid cooled fighters couldn't hope to match.
The weight difference would do very little, if anything, as far as performance at typical ETO fighter intercept altitudes of 25K and higher. It would have a measurable impact on range. None of the designs had a prayer of equally the remarkable overall capabilities of the P-51, even the very late war P-47N, while having greatly increased range of up to 2,000 miles in combat trim, was nowhere near as nimble a fighter as the Mustang,
It is, however, worth remembering that the mainstay of the U.S. throughout the 1960s and early 1970s, the F4 Phantom, was, in fact, a "Navy" design. However, in general the mission needs of the Navy and USAF as quite different, something probably best demonstrated by the huge difference in both design philosophy and operational performance between the F-14 and F-15. Today, of course, you have the compromise of the skies F-35 variants (great plan that, design a monstrosity of an aircraft that fails to really fulfill either the Navy or Air Force's operational needs for tactical deep strike, and gives the USMC a stealth design with all the limitations of the type, to perform close air support, the least stealthy mission an aircraft can perform).