No, The Constitution is a Compact between Sovereign States who are already Independent. The Declaration of Independence is the underlying platform of our Sovereignty.
Everything issue cannot be boiled down to a simple yes or no. Can an individual renounce his citizenship? Yes, if done legally. I can't make it any simpler or plainer than that.
Then your answer is that Rights ARE mere "Legal Privileges" enjoyed at the convenience of the Government, and that Rights ARE NOT granted directly to Individuals by God.
If an Individual cannot renounce his Citizenship at any time and for any reason whatsoever without obeying some "legal" procedure established by the Government, then it is the Government -- and NOT the Individual -- who is Sovereign. Your point of view is precisely what the Fathers of our Country fought AGAINST. Your view is essentially Communist.
And since your point of view establishes a Legal Barrier between the Rights of Man and the only True Sovereign ("No King but Jesus" -- the battle-cry of the Revolution), your view is essentially Atheist.
If a Man, created in the Image of God, cannot separate himself from Government without asking the Government's "Legal" permission -- then there is no ultimate constraint on the Power of Government at all. An Individual must have the absolute freedom to renounce his Citizenship at any time, for any reason whatsoever, because Rights are directly granted by God to Men as Individuals. To attribute to the Government the authority to obstruct that Natural Right in any way, on the basis of "doing it Legally", is nothing but Atheistic Communism.
Thank you, Sir. I' happy to see someone else understands this simple concept that the Founders wrote so copiously about:
That these are our grievances which we have thus laid before his majesty, with that freedom of language and sentiment which becomes a free people claiming their rights as derived from the laws of nature, and not as the gift of their chief magistrate.
Thomas Jefferson, Rights of British America, 1774