Possibly not, it is normal trend that when investors face severe downfall in their stock prices, they turn conservative and keep amount in liquid form rather than shifting it to other investment alternative.
However, prices of stocks depend upon several factors like performance of company, increased number of shares, etc. But prices of cryptocurrencies on other hand largely depends upon the influx/efflux of investors. So there lies a significant possibility that investors may turn to cryptocurrecnies if Stock market faces crisis.
I think it is not just easy for stock markets also to fall. And the market is just wathlist for the comodities if how much was sold or where to sell it. It doesnt really affect how the goods are produced or rather mined. Their are many markets that could use bitcoin and it is not just found in one place. Normally price should go down but i don't think a crash will ruin how bitcoin have helped and grown over the years.