Yes, statistically, that's what happens with corporation tax now, and according to AS at a press conference, will continue to do so. They'll pay corporation tax in Scotland on their activities in Scotland, and in England on their English earnings.
Setting aside my dislike of AS's growing habit of speaking on behalf of other people - a lot of the companies moving their head offices do most of their business outwith Scotland. So a significant proportion of the tax would go.
According to a Law Society briefing my manager was at, 90% of Scottish financial sector clients are in rUK, 94% of Scottish FS insurance products are sold to rUK, and 84% of Scottish FS mortgages are sold to rUK. There will be very little tax paid if you base it on activity.
Not scaremongering, just letting you know the approx splits (and I know you won't like this, but I don't think I can share the document, although the figures are probably recoverable with a bit of detective work that I don't have time to do just now)