No. It's the killing of the boss that advances raid difficulty and the flag for it is tied to the map, not the character. You could even carry boss heads (map A) to a world they've never been killed on (map B) and hang it on the appropriate sacrificial stone - giving you the ability to switch to their Forsaken Power without having to switch maps - and still only get the lowly "Eikthyr rallies the creatures of the forest" raid on map B.