Yes, diagonal 'castling' is permitted -- and necessary to the game.
If an even number of squares, each piece crosses the midline: a2-d5+f7-c4;
a1-a5+a8-a4; a3-a5+a6-a4; a4-a5+a5-a4.
If an odd number of pieces, the piece initiating the castling occupies the
midpoint: e1-c1+a1-d1; e1-d1+c1-d1; and so on.
Just like FIDE Chess.