Republic of Ireland sure went down the tubes being in the EU and using the Euro. It's not impossible for Scotland to work in much the same way as them.
The economy did go in the tubes initially and Ireland took like 75 years and a good 25 of them in what became the EU to become a tiger economy. But sure, it happened.
Also, about the remaining oil... Shetland and Orkney might prefer fishing regulations outside the EU and desire to remain in the UK.
Sure, ignore the economy in the short to medium-term and your largest trading partner for dreams of sovereignty.
Just don't be surprised if Shetland & Orkney want out if that were to happen, nor should we assume the people of Scotland will vote to leave, either, that flies in the face of most polls.
Also, a barely 50 percent vote to leave would have the same issue as Brexit. The areas near the border (including up near Edinburgh) are likely to wish to remain in the UK, which will cause resentment towards areas like Glasgow that are likely to wish to leave.
Edinburgh was once part of the ancient Anglo-Saxon kingdom of Northumbria and its name is an Old English anglicisation. In general, the people of historical Cumberland, Northumberland, the Scottish Borders, Lothian, Dumfries, and Galloway have a lot in common.