I wouldn't necessarily say that. Right now it's able to present itself to the electorate as the defender of Scottish interests in a hostile environment (Westminster). If Scotland became independent there'd be no need for that position anymore and a number of nationalist voters would probably move (back) to the other parties.
The same thing would probably happen in an independent Bavaria which I doubt would see the Christian Democrats run away with every election.
Would Scotland retain the British parties as they exist up there though? UKIP, for starters, would be irrelevant in their current form up in Scotland.
