I don't think this is the case.
This is a civil matter going through a private arbitration process, usually that's enough. Whatever the panel decides, doesn't necessarily mean there will be a criminal investigation. Was Roy Keane criminally charged for assaulting Haaland? Firstly someone has to complain to the right body (I think the DTI or Companies House). It also has to be in the public interest and there has to be sufficient evidence to prove false accounting. Is it in the public interest to punish City twice for the same thing? Add to that directors very rarely get prosecuted for anything like this unless HMRC think they're owed money or someone has directly lost a lot of money.
The two allegations relate to sponsorship deals (being worth less than stated and/or not paid by the sponsors but paid by a third party) and other third parties paying staff extra money (Mancini and Toure). I'm not certain that either of these are crimes (unless there are tax implications) even if they are true (I'm not sure they breach Premier League rules either!)
I might be wrong about the above, but the government haven't lost any money (in fact might have to repay City VAT/corp tax paid if this was proven) and no one has been directly hurt by it, so why would a criminal investigation or case follow? Who would pursue it?
I am not aware of the criminal courts over turning civil cases like this because by their very nature they are separate matters, between separate parties and have different burdens of proof and different rules/laws to assess them. Different outcomes are common, even if the fundamental issue is the same.
At the end of the day all this really is is a contractual dispute.
So no I don't think it is a fait acompli that a criminal investigation would follow.