//Given the result of the Brexit vote, does she have a compelling case?//
Brexit or not, she doesn't have a compelling case (to hold a referendum without the consent of the UK government). Constitutional matters are reserved for Westminster. That said, it is not unheard of for the Supreme Court to poke its nose into constitutional matters that are rightly reserved for Parliament, so anything could happen.
Personally, I don't see what all the fuss is about. It's quite clear there is nothing for the vast majority of the rest of the inhabitants of the UK from Scotland's participation in the Union (apart from a hefty bill). It was obvious that these delusions of grandeur would follow from Blair's ludicrous devolution arrangements; the Scots would never be content with operating the trains and emptying the bins. I nearly forgot running the ferries, so would many users of them I imagine considering the balls up the SNP has made of them.
If the majority of Scots are fed up with benefitting from the "free" services that an extra couple of grand per head brings them annually then it would be better all round if they just went their own way. It would stop them continually moaning about their lot and it might even get the ghastly Ms Sturgeon off my telly.