Was the Hughes H-4 Hercules capable of flying out of ground effect?
The answer can only be given by comparing it to other, broadly similar aircraft. My three references would be the British Saunders-Roe Princess, the Martin Mars and the Boeing 314 Clipper, all three at their time huge flying boats.



Obviously, the H-4 has the highest wing area relative to its installed power and its intended maximum take-off mass (MTOW), but does not look totally out of the range of the two smaller specimen. The Princess was conceived as a pressurized airliner and is of a more advanced design than the other three. With the lower wing loading come lower speeds, so the lower power loading looks adequate. Another huge military transport plane of that time which was derived from a cargo glider (the initial requirements asked for a cargo volume equivalent to a Reichsbahn standard cargo wagon) had a wing loading of just 150 kg/m², a very similar power loading of 23.56 HP/m² and flew just fine. Stick forces were massive, however, and stability was marginal.

The exact performance would depend on details like airfoils, aspect ratio, flap settings, hull design and stability, but in general it looks as if the H-4 would have been capable of flying out of ground effect. But its performance would not have been spectacular - a little more installed power would had made it better.