No they wouldn't. At least, not yet.
This is one of the myths that has developed on here the last few weeks. There is no requirement to report fraud to the relevant authorities at any particular time.
Also, the authorities aren't going to swoop into City's offices on the off chance the PL has some evidence. I am sure they are watching, though. And probably laughing ....
To be clear, the alleged breaches include providing the PL with accounts that don't give a true and fair view and acting in bad faith towards the PL. We are also assuming the substance of the alleged breaches is the same as CAS considered in the UEFA case. There is no direct mention of fraud.
Where fraud comes into this case is that the alleged breaches, taken together, effectively constitute fraud, so the IP will be required by the defence to take into account a higher level of cogency of evidence into their considerations than they would, say, for a simple PSR monetary breach.
All imho, of course, and I am happy to be blasted (again) by our legal guys if I have got it all wrong.