I'd say there is a good chance, but without knowing the UVW as delivered it is hard to guess. The GVWR is still only 14,500, even though it is on the E450 chassis, and that model has a lot in it, even before putting 7 people and all their gear, food & water onboard.
The Sunseeker brochure shows an estimated UVW of 12,500, but those are usually on the low side (before any options are added, or any propane in the tank or water in the lines and heater). That would leave at most 2000 lbs and seven people (average 154 lbs?) uses half of that. Water at 8.4 lbs/gal uses another big chunk. Visit a dealer who has one and get a reading of the UVW or OCCC (carrying capacity) off it, to get a better idea of what one of those can really carry. The RV will have an actual weight obtained as it left the factory. Odds are the OCCC carrying capacity is less than 2000 lbs as delivered.
You would be much better off with a small Class A in that size of RV, especially with that much to load onboard. A 30-32 foot Class A will probably have a GVWR in the 17,000-22,000 lb range. Not sure you will find one with bunks for 7 people, though.