No, absolutely not. The U.S. constitution always supersedes state constitutions. So while the state retains the right to regulate which firearms someone may own (and as the handgun issue has shown, this doesn't always fly) they cannot ban firearm ownership outright. That would be in conflict with the second amendment.

Its the same a state that did not have something in its constitution explicitly banning slavery. That doesn't mean you can own slaves there. And if a state did pass legislation setting up a framework for legalized slavery, the supreme court would smite it with its mighty gavel of judicial pwnage.