Can the act of "castling" happen even though... the rook moves through the "attacked" or "threatened" & the King does not...?
Yes you can castle even though the rook moves through a threatened square.
You may castle if the Rook is attacked or must cross a square that is controlled by the opponent (the latter only occurs in Q-side 0-0-0 where the b1/b8 square is controlled). The King may not castle out of check, into check, or across check.