Not exactly - there's a competition in Scotland between the British and Scottish identities, which means neither is ever truly dominant, and there's probably something of a void between the two for each person to fill in themselves. The monarchy is central to the mainstream British identity but isn't really a part of the Scottish identity. In contrast, in England there's almost no differentiation between British and English - it's a unity of messaging which leaves very little space for anything else. Probably the only time English people will differentiate between British and English is during an international football tournament, and what song do they play before every England game? GSTfuckingQ.
So even if an English person feels more English than British the chances are they will still identify with the monarchy. And so will everyone around them, regardless of their political inclinations on other issues. That's just not the case in Scotland.
There's basically no opportunity for someone south of the border to identify with their homeland without also identifying with the royals.