While I do think he would rather die than work for Kaido, I don't agree with the last part.
Kid doesn't care about the Alliance, what he cares about is himself and his crew. While surrendering to Kaido is not an option, taking his crew and fleeing Wano is. If it means getting out safe and sound, then I think he would do it.
The fact we're approaching mainland Wano should provide him the opportunity to do so.
Oda has frequently alluded to the fact that pirates betray each other, what better way of making this a reality for the SHs, by having Kid 'betray' the Alliance?
Plot wise, this would be better in the long term as it would create more animosity between the Straw Hats and Kid Pirates, especially if Luffy and Kid are meant to be proper rivals.