If they can make a case for it, and if they can enforce it with blood and/or treasure, then yes.
This either means something, or it doesn't:
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
If it doesn't, we're effed under the current regime.
Then you are talking about The Right to Revolution, not unilateral secession for what ever reason you choose.
I believe that under the Constitution, states could legally secede if that secession is agreed to by the other parties to the national contract. A simple reversal of the Statehood provisions written into the Constitution.
In my readings, if the South had taken that route in 1860, and petitioned congress to that effect, they probably would have been successful. They chose instead a route that guaranteed war. They were very foolish and arrogant men.