Not really sure. Probably doubt it.

Fausto would, he’d be the one to plan out ahead of time, he’d already have strategies for the E4 by the first gym leader

Wily for sure would, he's too methodical and paranoid. Dude would be running damage calculations and shit before stepping into a gym.

Uhhh probably not Summer since she makes a lot of rookie mistakes early on. Early in her journey she scrapes by with determination, and her ability communicate with Pokémon. It made giving commands a lot easier and increased her coordination with her team.

Yes because one of them is literally a nuzlocke character that I threw in (Will Jagger from my ooold X run)

No.

Yes. Given Nuzlockes are primarily the same as Competitive Battles, Elio would survive (and most likely thrive in) a Nuzlocke if he was forced into one. But in that case, he would use a new team altogether given the "faint = death" rule, and he's waaaaaay~ too attached to his current melanistic team for him to subject them to such a horrendous rule.

Mary doesn't really do competitive battling outside of contests, so I'd imagine she'd be fine. And a nuzlocke would be a lot more...personal for Jin. Not for angsty reasons, but because she'd want to be squaring up with the pokemon herself.