I haven't heard of such a thing, but it seems entirely possible.
We know that aspiration can cause dissimilation, as famously seen in Grassmann's Law for Greek and Sanskrit (an aspirated consonant becomes deaspirated before an aspirated consonant in the next syllable;
/h/ deaspirates into nothingness).
We also know that it can cause assimilation, if you interpret spellings like Ancient Greek χθ φθ as representing
/kʰtʰ pʰtʰ/ rather than
/ktʰ ptʰ/ (which many do). In this case, the fact that κ + θ at a morpheme boundary becomes χθ indicates assimilation of aspiration.
And we do see long-distance voicing harmony, where certain types of consonants must agree with each other in voicing. Voicing and aspiration are at their core two sides of the same coin.
So while I can't think of any specific examples of "aspiration harmony", it seems eminently possible, and I wouldn't bat an eye if I saw it in a grammar.