Probably not. The linguistic ancestors of the Greeks would not have entered Greece yet but they would probably still have been farther north and west than any Semitic population I've heard of, especially from before the Phoenicians started sailing....six millennia old or more. Was Greek neighboring the Semitic world at that time?
No. You're presumably thinking of the modern pronunciation, but, back when the Romans started transliterating Greek words into the Roman alphabet, it was an aspirated plosive (kʰ). The Romans rendered the Greek letters Chi, Phi, and Theta as "ch", "ph", and "th" because that's how they sounded: a plosive (c/p/t) followed by an "h". And that's thousands of years after the time you describe. Backing up those extra few millennia puts us into the era of Proto-Indo-European, when those sounds were still voiced (gʰ/bʰ/dʰ). The closest Semitic thing to PIE gʰ would have been "g", or "g" followed by "h".Was Greek χ of that time pronounced similarly to Semitic ḫ?
If the transfer happened during (or before) the PIE era (which is indicated by the presence of cognates in other IE languages), a laryngeal is the obvious choice, which means it would not exist as a consonant anymore by the time Greek becomes Greek, and its former presence would be detectable only by its lingering influence on the adjacent Greek vowel.Borrowing from Semitic to IE introduces similar questions, e.g. how would the Semitic ḫ ח ح be realized in early phase of Greek or another IE language.