It seems quite plausible to me that Welsh could have added the w, and since Hebrew doesn’t even use the Roman alphabet, it doesn’t really matter where it came from.
Languages don’t just “add” sounds like that. There has to be some explanation for the existence of a sound. In the Classical Greek word aêr there is no labialized environment that would allow for a labial [w] glide to intrude between vowels–Welsh doesn’t insert sounds like that. All we know is that the original [w] sound disappeared from Classical Greek, though it had existed in earlier stages of Greek.
The alphabets, Hebrew or Roman or Greek, are totally irrelevant to this question, since we’re discussing the sound itself, not how it was written. Linguistic borrowing takes place whether or not writing is used.
When English speakers think they hear “phlegm” in other languages, they mean the velar fricative /x/, the sound of the “ch” in Bach. (If you listen to classical music radio, nowadays the DJs are making an effort to articulate the authentic German pronunciation /ba:x/, and some of them actually succeed.) Irish and Hebrew both have this sound (as well as Arabic, Azerbaijani, Breton, Chinese, Dutch, German, Greek, Persian, Polish, Brazilian Portuguese, Russian, Spanish, and many many other languages around the world), even if it sounds outlandish to your monolingual Anglophone ears.
The way I see Irish phonology, it is dominated by the opposition between “lean” and “broad” consonants. The lean sounds are palatalized, in the front of the mouth, and occur next to the vowels e and i. The broad sounds are in the back of the mouth, sometimes labialized, and occur next to the vowels a, o, and u. This is why there are so many silent letters in Gaelic orthography: sometimes a silent e or i is inserted to show that a consonant is lean before a back vowel, or a silent a or o is used to show that a consonant is broad before a front vowel. Lithuanian also uses silent i to indicate palatalization. Since the opposition between palatalized (“soft”) and nonpalatalized (“hard”) sounds is characteristic of Russian, the sound of Irish reminds me of Russian more than anything else.