Can a seaplane make a long distance sea voyage on the sea?
Not very well. If we look back to the 1930's, the age of the large flying boat airliners, they were designed to take off and land in minimal sea states - no more than 3 foot swells. Typical usage would be in large rivers or protected bays, and the flying boat was used because long runways weren't available. Nor did those airliners tend to stay on the water for long, usually they were brought onto land with beaching gear if they weren't in service. 

The problem is - an aircraft on water is highly susceptible to changes in wind - it is, after all designed specifically to use flowing wind to remain airborne, so gusts of wind while on the water will have a stronger effect on an aircraft than they would on a ship. As well, the aircraft's hull in the water tends to anchor it, subjecting the airframe to stresses from wind in varying directions, that it wouldn't encounter while flying. 

Amphibious aircraft and the pure flying boats, left on the open ocean, tend to become damaged to the point of becoming non-airworthy. 

Couple of examples:

While on lifeguard duty off of Truk during WW2 and landing to pick up a shot down pilot, Lt John Dowdle's OSU-2 Kingfisher had overturned due to a gust of wind. Lt John Burns also lost his Kingfisher due to the hull springing leaks from being pounded by waves, while he rescued Dowdle and the downed pilots. Both Kingfishers were lost, but their crews plus the airmen they had rescued were saved by submarine USS Tang, in an epic lifeguard mission that saw Tang pick up 22 aircrew. 

The Bermuda Sky Queen, a Boeing 314 formerly known as the Pan American Capetown Clipper, ran short of fuel while flying from Foynes, Ireland to the US. It did survive for over 24 hours on the ocean before the 62 passengers and crew could be rescued, but after that much time on the open ocean, the plane was coming apart from the pounding of the waves (the tail section was starting to come loose) plus damage from colliding with the Coast Guard cutter picking up the people. As a result, the Bermuda Sky Queen, the last airworthy 314, had to be scuttled.