Maybe. Today I listened to the Fifth string quartet, and thought, why even say it's in F sharp minor when there are so many accidentals, right from the get go?
Perhaps it's a little less extreme in the Hiller Vars, but it's there allright. So there is the robust 9th variation, Allegro con spirito, but there is a Trio (starting at 23:58 in the video) that is heavily chromatic. So maybe it is part of the character of the Variations, this competition between diatonic and chromatic.