It's extremely likely most, if not all, of their top players force a move if they are relegated.

One, City probably wouldn't be able to afford their current salary bill in the Championship with no Champions League, especially now that they're actually under FFP scrutiny and a lot of the remaining legitimate sponsors will try to distance themselves from this scandal. TV money is also a ton less in the second division. Tickets sell for less, and they will likely sell fewer of them. They will sell less merch. They would probably be deemed ineligible for parachute payments. We're talking a huge drop in revenue.

Two, players don't like "wasting" a season in a lower division than where they should be playing. Not to mention there's no "guarantee" it will only be one year... if one key player jumps ship the rest will soon follow and promotion might prove to be harder than expected when you're trying to integrate a bunch of new players. Especially since if they are relegated, it means a minimum of two seasons without Champions League. They'd likely have to have a fire sale to offload their highest earners and guys who simply don't want to play in the Championship and miss Champion's League.

If they could manage to hang on to their important players for that season, then yes it kinda fucks over the teams that are in the Championship as it's basically a guaranteed promotion spot gone, leaving the rest of them to fight over the remaining two.