The SNP are not totally anti anything which is English. There are some things they like about the UK and wanted to keep in the UK, for example, the pound. In fact I remember a common counter argument to the SNP during the independence referendum was "if you want to keep so many things from the UK, why not just stay in?" The Queen definitely falls into that category.here's what i get about the SNP: their disdain to for everything English and London-based, could possibly trump everything else. So, the possibility of a legitimate male-line descendant of the House of Stuart, that moves back to Scotland in the 1920's (right after his benefactors where deposed after ww1), and his great-grandson is now living in Scotland, becomes the SNP's flag bearer for complete separation from england – including its London-based Queen.
In the current political climate I cannot see the SNP selling the royal family (but not the principle of monarchy) as another part of the Union which is wrong. I find it even more unbelievable that a party in a western country would set up a completely new monarchy with an entirely different royal family. I think that would be step too far for many on the right, let alone in the SNP, which is a left wing party and likely has a large number of republicans in it already.