What would happen if all the people who agreed to accept it would also want to withdraw it from their accounts at the same time?

If everyone continues to agree it's worth what it says then not very much. Of course the whole thing can collapse for a number of reasons, not much different from other mediums of exchange that don't have an intrinsic utility, the utility is a sufficient number of people willing to cooperate. Which is pretty much everything except bartering goods.

withdraw for what? for fiat(=fake) paper bills, or for similarly fake digits on a mobile app?

Doesn't matter that much really. Basically just "take it out of the bank" somehow.

It matters. Do you want digital bits? You can have all the bits you want, and so can the entire population of the city.

Do you want physical cash? Well, of the bank is printing its own, they can hand out whatever they can print.

If you expect fiat currency (e.g. USD) or precious metals, then withdrawals are all limited by what the bank has on-hand, or can get quickly. Assuming this is what you’re asking about, it would be a “run” on the bank, they’d close up shop for the day, and it would affect the faith the population has in the monetary supply.