Well, in a certain sense it does. If the consitution guarantees you certain rights that not even the state is allowed to remove, then secession is in effect removing you from the protections guaranteed under the bill of rights. A state cannot vote to ignore the constitution and secession is in effect doing just that.
Except that the Constitution is a compact between the various states and the Federal Government, in which in exchange for alliance with that government both parties agree to certain restrictions of authority. However, make no mistake, regardless of whether the original mechanizations for ratification of the Constitution were legal or not according the the Articles of Confederation, the fact that all states ratified the document prove de facto and de jure that the Constitution did need to be unanimously accepted.