It doesn't matter what I think. I try to research and there is no evidence that City have asked for a suspension. In fact there is a strong opinion that City have not asked as, by doing so would mean that CAS wouldn't expedite the case, with respect the squad planning etc that wouldn't be in City's interest
This is what LAW in Sport have outlined of the procedure This was pre the Covid 19 outbreak
Given the comparatively short time before the ban from UEFA competitions takes effect on Manchester City (i.e. the commencement of UEFA competitions for the 2020/2021 season in the summer of 2020), the parties may elect, by mutual consent, to an expedited procedure (pursuant to R52 for appeals and R44.4 for ordinary arbitration proceedings). If the parties cannot agree to expedited proceedings, a party can apply for ‘Provisional and Conservatory Measures’ under R37. For example, Manchester City may be able to apply for an order to the effect that the ban is suspending pending exhaustion of the CAS proceedings.