You can have a pure HCl, even as a liquid, but it will be not an acid. Pure sulfuric acid contains free (well, almost free) H+, liquid HCl is not dissociated. HCl is surprisingly covalent in its nature, that's why it is gaseous and not solid at STP.
In normal conditions you can't prepare HCl solution more concentrated than about 37-38%, so you probably won't get to the point where the conductivity goes down.