Not sure the point of this question since the states were involved in a war, that in itself would be the deciding factor.
Not sure that the CSA Constitution denied them the right. The United States Constitution did not prohibit the act of secession. However being the CSA was engaged in a war this would surely have been used
Article III
Sec. 3. (I) Treason against the Confederate States shall consist only in levying war against.them, or in adhering to their enemies, giving them aid and comfort. No person shall be convicted of treason unless on the testimony of two witnesses to the same overt act, or on confession in open court.
On the other side of the coin Lincoln had no problem ignoring the United States Constitution.
Here is a history of West Virginia--
http://www.wvculture.org/history/statehoo.html
Following a Union victory at the Battle of Philippi and the subsequent occupation of northwestern Virginia by General George B. McClellan, the Second Wheeling Convention met between June 11 and June 25, 1861. Delegates formed the Restored, or Reorganized, Government of Virginia, and chose Francis H. Pierpont as governor. President Lincoln recognized the Restored Government as the legitimate government of Virginia. John Carlile and Waitman T. Willey became United States Senators and Jacob B. Blair, William G. Brown, and Kellian V. Whaley became Congressmen representing pro-Union Virginia.
On October 24, 1861, residents of thirty-nine counties in western Virginia approved the formation of a new Unionist state. The accuracy of these election results have been questioned, since Union troops were stationed at many of the polls to prevent Confederate sympathizers from voting. At the Constitutional Convention, which met in Wheeling from November 1861 to February 1862, delegates selected the counties for inclusion in the new state of West Virginia. From the initial list, most of the counties in the Shenandoah Valley were excluded due to their control by Confederate troops and a large number of local Confederate sympathizers. In the end, fifty counties were selected (all of present-day West Virginia's counties except Mineral, Grant, Lincoln, Summers, and Mingo, which were formed after statehood). Most of the eastern and southern counties did not support statehood, but were included for political, economic, and military purposes. The mountain range west of the Blue Ridge became the eastern border of West Virginia to provide a defense against Confederate invasion. One of the most controversial decisions involved the Eastern Panhandle counties, which supported the Confederacy. The Baltimore and Ohio Railroad, which ran through the Eastern Panhandle, was extremely important for the economy and troop movements. Inclusion of these counties removed all of the railroad from the Confederacy.
In terms of the constitution itself, the subject of slavery produced the most controversy. Delegate Gordon Battelle proposed the gradual emancipation of slaves already in the state and freedom to all children born to slaves after July 4, 1865. Although some delegates opposed Battelle's position, they knew they could not create a pro-slavery document and gain approval from Congress. Following much debate and compromise, the provision written into the constitution banned the introduction of slaves or free African Americans into the state of West Virginia, but did not address the issue of immediate or gradual emancipation.
The United States Constitution says a new state must gain approval from the original state, which never occurred in the case of West Virginia. Since the Restored Government was considered the legal government of Virginia, it granted permission to itself on May 13, 1862, to form the state of West Virginia.
When Congress addressed the West Virginia statehood bill, Massachusetts Senator Charles Sumner demanded an emancipation clause to prevent the creation of another slave state. Restored Government Senator Carlile wanted a statewide election to decide the issue. Finally, a compromise between Senator Willey and Committee on Territories Chairman Benjamin Wade of Ohio, determined that, after July 4, 1863, all slaves in West Virginia over twenty-one years of age would be freed. Likewise, younger slaves would receive their freedom upon reaching the age of twenty-one. The Willey Amendment prohibited some slavery but it permitted the ownership of slaves under the age of twenty-one.
The United States Senate rejected a statehood bill proposed by Carlile which did not contain the Willey Amendment and then, on July 14, 1862, approved a statehood proposal which included the Willey Amendment. Carlile's vote against the latter bill made him a traitor in the eyes of many West Virginians and he was never again elected to political office. On December 10, 1862, the House of Representatives passed the act. On December 31, President Lincoln signed the bill into law, approving the creation of West Virginia as a state loyal to the Union without abolishing slavery. The next step was to put the statehood issue to a vote by West Virginia's citizens. Lincoln may have had his own reasons for creating the new state, knowing he could count on West Virginia's support in the 1864 presidential election. On March 26, 1863, the citizens of the fifty counties approved the statehood bill, including the Willey Amendment, and on June 20, the state of West Virginia was officially created.