I am not quite sure what you mean by "are you trying to copy the id's of the associated entity(s)?? .. or perhaps does the definition of the associated hatch refer to the bounding objects ??".
I am assuming that Hatch.GetAssociatedObjectIdsAt( int index ) returns the objects associated with the loop with the given index (in this case I assume the id of the rectangle is returned). In the code I just posted I am making a new ObjectIdCollection with the same object ids as in the original loop in order to create an identical hatch loop (i.e. in this case it is associated with the same object(s) as the original one).
If I haven't misunderstood completely, by definition an associative hatch refers to the bounding objects.