I recently came across an alternative possibility:
“Even the derivation of the term is not simple. It probably derives ultimately from the name of the Greek philosopher Epicurus, but Rabbinic literature displays no knowledge of the existence of a Greek philosopher by that name. If it were a semitic term, it would be derived from the root pqr, which by an apparently fortuitous coincidence means licentious, dissolute, or rebellious. This derivation has been maintained by at least one eminent philologist.”
And: “The fact that the Amoraim derive the term Apiqoros from the Hebrew root pqr (Sanhedrin 38b) provides some evidence that they were unaware of Epicureans at all. But on the other hand it may only be an example of self-consciously creative homiletic Rabbinic exegesis.”*
Thus it could be – although Danzig seems to think probably not – originally at least, a “phonetic coincidence.”
* Gabriel Danzig, “Epicurus and Epicureanism in Rabbinic Literature” in the Oxford Handbook of Epicurus and Epicureanism; Philip Mitsis, Editor.
Classical Hebrew is based on such consonantal roots, and words that are so based -- even with the root letters rearranged and with additions -- are etymologically related.