I don't think that will happen but if City's punishment was a points deduction tantamount to relegation, they would appeal immediately anyway. It's impossible to know what will happen there.
I think the problem for City is two-fold.
Whereas other teams in the Prem have basically put forward their case in mitigation when accused of financial breaches, City have disputed every single charge. That will not have gone down well with the PL Management, as it has cost the PL £millions.
In a time when the PL is under pressure re a Regulator, I believe the last thing the PL want to do is to be seen as being weak and not able to control any club within their ambit That would play right into the Government's hands. And I believe that the PL CANNOT go soft on City if a sizeable chunk of the charges are upheld against them.
Also to answer one of your points, if a massive deduction meant they were relegated, any appeal is likely to be fast-tracked in order not to create chaos for the start of the 25-26 season.