Let’s examine this rationally.
Should Scotland gain independence they can certainly continue to use the Pound. There is nothing to stop any nation using another’s as currency. Of course, whether they will have sufficient ongoing income to obtain more pounds once their initial holding has run out is open to debate.
However, if (and it’s a very, very big if indeed) they gain EU membership:
(a) They will have to adopt the euro (there are no opt outs for new members)
(b) They will have to join the Schengen area if it still exists(ditto)
(c) The question of whether there will be a border between the UK and an independent Scotland is not a decision for them to make.
With relation to (c) if Scotland does become a Schengen signatory I cannot see how the UK can fail to impose border controls.
Ms Sturgeon seems to be under the impression that Scotland will be welcomed to the EU with some sort of “reserved rights” as having been a (small) constituent part of a former member nation. I think she may find that it does not quite work like that and the five current EU candidate nations may feel justifiably aggrieved should Scotland jump the queue. They will also be somewhat miffed if Scotland is afforded privileges that are not open to them. She also seems to fail to grasp that the main reason the EU wanted the UK in its fold was because of the wealth and business created principally by England. This is not trumpet blowing because I am English, but a plain fact. Although the EU seems to welcome all and sundry to its clutches somewhat regardless of their prospects, they may be reluctant to give priority to an area that generates far less than half the wealth of London.
The Scots would be wise to bear all this in mind when they cast their votes, should they be granted a second referendum. Furthermore, Ms Sturgeon needs to heed the fact that, although all areas of Scotland voted to remain in the EU, almost 40% of those who voted said they wanted to leave. Presumably that same 40% would not be too happy to be part of a UK that left only to find themselves in a Scotland that wishes to rejoin.
As I said yesterday, it is hard to understand why Scotland seeks independence from the UK but is more than willing to throw its lot in with a broken, shrinking institution of which they would form but a tiny part. But, as they say, there’s now’t so queer as folk and Scottish Nationalism has never been too renowned for its clarity of thought..