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.