I think that depends a lot on what you mean by "the crypto market." In a lot of ways equity stocks are already ownership tokens, and in terms of functionality a blockchain approach to holding and trading them would make a lot of sense. I would be surprised if, ten years from now, there wasn't some sort of method of cryptological ownership underlying the stock market. 

Does that necessarily mean it will look much like cryptocurrencies as we know them now? Probably not. We have some ownership tokens around, but mostly the well-known coins operate as something closer to currencies, and wouldn't be very useful in the context of owning part of a company. 

But remember that blockchain technology can be used by anybody, and it can do a lot of things that aren't currency. It's particularly well-suited for tokenizing things of real value and allowing people to trade them easily and simply. Which is also the purpose of the stock market, so they seem like a natural fit for each other.