In 2013, when the original Silk Road was shut down by the FBI, Bitcoin price decreased, at that time compared to today Bitcoin adoption was too low, but today even if a small percentage of Bitcoin is being used in deep web, it is nothing compared to what is being used for legal purposes. First of all it is almost impossible to shut down dark net, all the sites aren't illegal. Today or tomorrow, even if majority of illegal bitcoin accepting deep websites are shut down, I don't think it would have any serious impact on bitcoins price.