I don't know. Some of the clauses in the US constitution make me think that unilateral secession from a state was not allowed in any state constitution in 1787.
Another factor to consider in relation to the transfer of counties from Virginia to West Virginia is Article Four, Section 3 of the United States Constitution adopted in 1788.
New States may be admitted by the Congress into this Union; but no new State shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or Parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
So the Federal Constitution of 1788 would seem to override the Virginia constitution of 1776.
Note that Article Four, Section 2 says:
The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
So if citizens of Virginia had the right to unilateral secesssion from Virginia, the citizens of every other state would have the right to unilateral secession from that state.
And Article VI says:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
This indicates that if the Virginia constitution made unilateral secession from Virginia legal, Article Four, Section 3 would override it and make unilateral secession from Virginia unconstitutional.
So if unilateral secession from Virginia (or any other state) was constitutional according to that state's constitution in 1787-1789, Article Four, Section 2 would make it constitutional in every other state, while Article Six and Article Four, Section 3 would forbid unilateral secession from any state.
So I deduce that if the constitution of any state in 1787-89 made unilateral secession from that state legal, the United States Constitution that was written and adopted in 1787-1789 would have contained contradictory clauses. I find it a little hard to believe that a bunch of politicians familiar with the constitutions of their respective states would have overlooked any contradictions in those articles in the US constitution they were writing.