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What would be the concequences of an independent Virginian Republic, beyond the obvious fact that the Northern Virginia wouldn't be the main front? I'm assuming that Virginia declares it's neutrality in the conflict.
Also Lee may or may not stay with Virginia. He wouldn't be crossing swords with them...
Also Virginia only has to stay independent for the duration of the war. Some time after the war Virginia can rejoin the Union. West Virgina can decide to secede from Virginia.