I don’t think the Monarchy would be in any danger in the short to medium term of any independence. The SNP doesn’t have Republicanism as part of its manifesto. Remember, it was the Scottish Crown that took over the English throne, not the other way around.
As for the Jacobites being invited to take over, well, Jacobism these days is nothing more than a romantic fantasy and not the serious political movement it was 300 years ago. None of the Jacobite heirs has claimed the throne since the early 19th century and have not expressed any interest in reviving that claim now. Apart from anything else, the fact that the Jacobite heirs are now actual de-facto and dejure sausage-sucking Germans makes the common Jacobite criticism of the present Royals being ‘German interlopers’ because they are descended from the Hanoverian electors seem absolutely ridiculous....
I think anything can happen. From what I have seen at work, the Scots could be pretty pragmatic and skeptical when needed, but they are also very empty-headed and emotional when it comes to talks about nationhood and symbolism. I believe they are capable of being that reckless to go for the Jacobite monarch if Scotland does become independent.
Of course, we in the Commonwealth needs to prepare for the worst. “Who will be our head of state” may not be a mere academic exercise.