I believe that after Irish independence, the IRA was focused on the counties in the North, which remained in the UK.
Scotland would go lock, stock and barrel.
It turns out that applies to NATO, too. And would the current government actually want to be in NATO? So I guess Scots independence isn't really in the US interest.
There's a lot of romantic interest attached to the idea of history being made, but a lot of history has been made in our lifetime, and when it actually happens a lot of the time we don't actually notice.