The King wins the revolutionary war if he conquers all your coastal colonies. Since there are no amphibious attacks in Colonization, a possible strategy could consist on blocking the access to one of your coastal colonies so the Loyalist army can never land. However, this doesn’t work, as any military units blocking the way will be removed to make space for the king (undoubtedly to prevent this). Funnily, this also applies to any units from other European nations: all their pesky dragoons stationed next to your coastal colonies will magically vanish when the Independence war starts.

But does this apply to Indian villages as well? In the attached picture, there is no way to land next to the colony of St. Louis without declaring war on the Iroquois first, since the only adjacent land tile is occupied by a Native village. What would happen if a human player settled a colony there and declare independence? Would the village disappear automatically? Would the King attack the Iroquois?

(That was not my colony; in this game I was playing as Spain so I had no chance to experiment what would happen).

Really good question.
Oh and not only military units, any type of units.

Maybe this will get you division by 0 Error :D

And no, never tried this or have had it :D

Maybe that is how they actually won the war ;). All the history is a lie ;P.
The king arrived seen there was nowhere to land and just went back to Europe