Wiktionary is your friend:
calx is probably from χάλιξ chalix: “pebble”:
Unknown, perhaps Pre-Greek. Probably cognate, ancestor, or descendant of Latin calx (“limestone, chalk”)
χαλκός “copper”:
Uncertain. Has been compared to Proto-Slavic *želězo (“iron”), Latin ferrum, and Hittite [script needed] (ḫapalki-). Perhaps related to κάλχη (kálkhē, “purple”). Ultimately, Proto-Indo-European origin seems unlikely and the word is probably a borrowing.
… So if calx is indeed from Greek, we have a non-Hellenic chalik– stem for “pebble”, and a non-Hellenic chalk– stem for “copper”.
We can’t rule out that they’re related somehow; and copper and limestone are both, um, minerals. But… probably not.