It existed in the sense that the Confederate States of America existed. A bunch of politicians unhappy about the countries government went into rebellion, coincidentally in the south, and then the fireworks began. But as a cultural concept, neither the CSA nor South Vietnam existed before their respective political rebellions aka they weren't "real countries". And after the rebellion was crushed they don't exist anymore in any real cultural/political fashion. If they won, they would have developed into real distinct countries eventually, but they never got the chance.

As far as invaders go, both sides invited so many vistors and advisors its hard to say who that is.