People have made harmoniums with modifications to play the 22 shrutis of carnatic music, and with those you can probably more or less approximate the right tone

People have made harmoniums with modifications to play the 22 shrutis of carnatic music, and with those you can probably more or less approximate the right tones for most hindustani raags too, but it's rare, your average harmonium probably just does bog standard western-style equal temperament. As the article says though, the main limitation of this kind of instrument is that it cannot generate glissandos (meend) and ornamented notes (gamaka).