of course it can greatly affect the price of crypto currencies on the market, especially if the holders of crypto currencies are citizens in the countries where they live do not accept bitcoin as a means of payment transactions. so that if something happens with their FIAT currency because of a crisis they will prefer to secure their FIAT currency compared to the crypto currency they have. and indirectly it will affect the price of crypto currency.
I agree, depends on WHEN the crisis strikes and at which level the development and acceptance of crypto currency is by then. In more countries, fiat is the only source of payment.