At the time of its appearance btc was something new and unprecedented but now the maximum that can we hope for is growth due to a lot of new users who will want to buy a ticket to the moon in the middle of all this depressive crisis.
If this does not happen, then Yes, BTC will go down as well as the rest of the market because people will not have money and absolutely will not want to try to make them on risky investments (and for most people, cryptocurrencies are just risky investments)
I don't think bitcoin will fall immediately and/or significantly, because it is the safe haven for a lot of people from developing countries.
So at the point when economy of developed country will be in danger - btc will be supported with money from poorer people out there.
So, poor people will keep btc from falling sharply? But they will not keep it from falling slowly, and it is unlikely that "poor people" will invest money in something that they certainly do not understand.
Not just that they don't understand , and maybe they do, but they can't afford to risk that much and lose a bit of money that they actually don't have enough. So, this is not likely scenario.
Besides, traditional economy and financial system and Bitcoin market are not directly connected so we can't say what exactly will happen when full economy crisis starts, there is no good prediction for that.