Unfortunately no, they are not compatible.  Every mod has its own set of what they call "global variables" and the engine reads the saved values of those variables when you load the save.  To make New Horizons work with a newer version of the engine, many of the global variables had to be either removed because they no longer work (like for the sea and weather) and replaced with different ones.  So those global variables no longer match the original order or type of value.

However, nothing had to change with COAS or GOF mod, so if someone had old saves, with the original engine, for those games, they are compatible and can be played.  But POTC, Caribbean Tales, and New Horizons were built around a different game, where the weather and sea conformed to an older version of Storm and they had to be altered in that manner of global variables I described.