Yes, double flats and double sharp notes are dependent on the key signature, and written as accidentals so that they don't alter the notes used by the key signature (and we are never allowed to do that, are we!)

A classic example that comes to mind is Moonlight Sonata, Opus 27 by Beethoven. Several bars have notes such a F double-sharp and B sharp because it is incorrect to change the notes of the key signature (C#min)
Trev

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