Hm, I think most other EU countries would not care as such if the UK splits. Perhaps Spain and Belgium might see it as bad examples.

But the more interesting question is how a request to join the union from an independent Scotland would be treated (as it is the state of the UK, not its territory that are members today an independent Scotland would formally start outside the union (barring re-interpretation of rules)). Since Scotland would fulfill all requirements (legislation already in line with EU directives) the only thing that could keep it out is if some countries would try to block it.

So I guess it boils down to if the government in London would protest. Would it?

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Surely it would be less of a problem that German unification, which brought in lots of new people to the union.