It would be, medium to long term, a signal to diverge.
So that'll be a floating currency and goes back to my further point that Scotland will only have a weak, minor reserve currency with no financial history. This will make borrowing more expensive for the government, businesses and the population as a whole. The weaker currency is indeed imperative for Scottish business exports but it will result in a lower standard of living in Scotland, which is not widely advertised to the electorate it would seem but it's inevitable.
What is also being overlooked is incurred debt, Investors will have majoritively BoE guilts and a smaller (yet to be calculated) amount of new BoS bonds. The new BoS bonds will have to pay out more to match the stronger Stirling or you risk investors scrambling for Stirling Gults, and that will further hurt the Scottish economy.
Your further statement that an independent Scottish currency will be able to protect depositors as well as they are currently doesn't seem to stand up for me. Do you have more insight into how it will other than the short line you gave?