Article XVIII: Every State shall abide by the determination of the United States in Congress assembled, on all questions which by this confederation are submitted to them. And the Articles of this Confederation shall be be inviobly observed by every State, and the Union shall be perpetual; nor shall any alteration at any time hereafter be made in any of them; unless such alteration be agreed to in a Congress of the United States, and be afterwards confirmed by the legislatures of every State.
Yes, we later changed our form of government, when we adopted the Constitution. But the Union we formed persisted, and the individual States had no more authority to unilaterally secede under the latter than they did under the former.
Be that as it may, the South would have been allowed to secede, had it not decided to begin open warfare against the Union.