In this case could the central banks print more money to cover the rush and prevent a collapse?
Sure, a bank could borrow from the central bank, such as the Federal Reserve, which in this case is known as a "lender of last resort". This is more-or-less what happened during the 2008 financial crash when the banks were "bailed out". It introduces a number of problems, not least the fact that the tax payer ultimately has to bear the burden of the bail out.
In the modern day money is created via credit (it is called credit money for a reason).
Correct. It is fully known as the "credit theory of money". To follow on from my example of fractional reserve above, in credit theory the bank doesn't even need a deposit to start lending out. They simply create a $100 credit of new money in your account, whilst at the same time debiting you $100 in a new payment request. From the bank's point of view there has been no net change; their reserves haven't changed and their balance book still has the same bottom line. However, $100 of new money has just been created.