Yeah, it's unarguably a convenience of war. Many states had large groups of population that were still loyal to the union and no better example exists than Virginia, where the Appalachian area was overwhelmingly pro-union. However, it's equally clear that they were not the legitimate government of Virginia because they only represented a small minority of Virginians (if they were the majority, Virginia wouldn't have seceded). The Constitution says that a new state cannot be formed from the territory of an old state without its permission, so there had to be a legal fiction where a new government of Virginia was recognized and that government then consented to let part of its territory (the part the new government was located in) to form a new state. Regardless of result, it's hard to argue it followed the spirit of the law.
That being said, it does demonstrate the difficulty of secession. Once you can establish that disagreements between winning and losing groups in a democracy are sufficient to justify secession, you open yourself up to counter-secession by any group that disagrees with the majority in the newly seceded state.