ICE strand is array per point, point is 'context parent' of sub - array of strand positions. While strand positions are not affected by transforms of point, point still represent the first position, before strand array starts. If you already have your set of points, generated by ICE or something else, perhaps the most elegant way is to create another point cloud, containing only one point, and array of strand positions, like in picture.
Each point is carrying the strand array - so if you really want just one point cloud for everything, probably you'll need to delete the all but one point at the end of ICE tree, for something like in picture.
