Here's my penultimate thoughts on the Carolina situation:
From a purely practical standpoint, yes the Union could annex Carolina at any time. From a political standpoint the latest it could have feasibly done is the Early-Mid Custer Era. By the time of the World War on, the Union needs their allies to act in sync. At this point it sets a horrible example if you reward a century of loyalty with "lol bordergore, time to invade." None of America's allies would want anything to do with them at that point. I'll also point out that the Union might not want to face the prospect of bloody mountain warfare less than 8 hours from the capital of NUSA. The Appalachians could very well become a small Vietnam, but you can drive by and see it. Finally, absorbing millions of old-school Southron white supremacists could cause old wounds to rise up across the South.