The 1st Edition YY rules weren't really that well thought out (after all, we didn't realize it was a playable game until several months after publication). When 2nd edition came around, we actually tried to make the costs for doing different things make some kind of mechanical sense, which is where the 3 YY to reroll rule came in.

In actual play, I rarely pay attention to the YY rules as written. Instead, the YY cost of X depends on how cool X is, how many YYs the player has, what it does to the story, and how much the player has annoyed or amused me throughout the game.

To answer Colin's original question: No, you can't do that. To go from a failed 17 to a successful 14 by the rules as written, you'd have spend 8 YY (3 for the re-roll, 5 for the auto success (which would technically be 15--1 YY for every 3 points of the success)).