France, Great Britain, and the USA are all "powers" that belong to the same Faction, the West. So, yes. A British ground unit in Algiers prevents the associated areas from becoming independent if France falls.
Fight Win Prevail - but enjoy the game whatever happens :D
Addtional question (sorry for me being so slow if during a later turn, that British Army (from your example) leaves Algier and so Algier becomes unoccupied, will Algier then turn to Armed Neutral or will it remain as a colony in the Western Faction?