It was - for a while - during the Jacobite rebellion, but ceased to be used even before the song became our official National Anthem. The other side of the coin that Scots neglect to mention is that there was a pro-Jacobite verse:
God bless the prince, I pray,
God bless the prince, I pray,
Charlie I mean;
That Scotland we may see
Freed from vile Presbyt'ry,
Both George and his Feckie,
Ever so, Amen.
Errr ... are you trying to claim that God Save the King (Queen) once had a verse about freeing Scotland from the king and praising his mortal enemy?! This has never been an actual verse of GStK/Q - it's a piss take.
I think people in Scotland sometimes boo GStQ in protest that a British anthem is being used as an English anthem. Not that most Scots would want to use it ourselves, but because it's a constant reminder that the English think of themselves as equivalent to the British, with the other home nations not being relevant/acknowleged. I would personally never boo an anthem but I still feel really annoyed every time I hear the English use this as if it were their anthem.
And it's also very weak to say that there isn't an English anthem. Make one up! Most countries anthems are pretty recent, no need to find a traditional old song to use.