In the Excelsior books that's exactly what happens. War Dragons states outright that Chekov was Sulu's original choice for 1st officer but the Khan incident played on his conscience too much, so he went back to Kirk, and post Khitomer, but after Kirk died (as far as their concerned), Chekov finally steps up as 1st officer for Sulu.
That's great. I've got to grab those. I was thrilled when Sulu finally made Captain and got the ship of his dreams. I'd love to read some of his adventures.