The short version is "it depends". Ford increased the E-450 tow rating to 22,000# to allow towing of up to 7,500#. However Jayco like all other E-450 manufacturers use up to a 5,000# / 500# hitch (some only put 3,500# / 350# hitches!) This can be resolved by adding a "sub-frame beef up" to your Greyhawk. Many hitch and tow shops can do this work for a reasonable price typically about $1200. They replace the hitch with a 7,500# hitch and install additional supports back to the Ford factory frame following Ford factory recommendations. My Greyhawk is labeled for a max GCWR of 22,000# so I can tow up to 7,500#. I wouldn't recommend towing a car hauler with a 750# tongue weight because it is so far back from the rear wheels even with a weight distributing hitch it would be hard to handle. I have seen people towing a full size F350 crew cab behind an unmodified Class C E450 but I would not. With the sub-frame beef up you are good to go.
2004 Chevrolet Silverado 3500 LT with a 2004 Jayco JayFlight 29BHS
2014 Greyhawk 31FS with a 2007 Tahoe toad
2014 Thor Palazzo 33.3 with a 2007 Tahoe toad