Yes, basically Greek words in English are pronounced as Latin loanwords, according to how the Greek words would have been pronounced in Latin around AD 1 (except that ph and th, but not ch, are pronounced as fricatives in English). Greek αυ and ευ were still pronounced as diphthongs at the time.
Wikipedia suggests that "ευ" was pronounced /eu̯/ in ancient greek[0]. My suspicion is that "ευ ζην" is an Ancient Greek "fixed phrase" which is pronounced with Modern Greek phonology.
Reminds me of Yog-Sothoth, which would be a great name for an anthropomorphized statistical model...
> Yog-Sothoth knows the gate. Yog-Sothoth is the gate. Yog-Sothoth is the key and guardian of the gate. Past, present, future, all are one in Yog-Sothoth. He knows where the Old Ones broke through of old, and where They shall break through again. He knows where They have trod earth's fields, and where They still tread them, and why no one can behold Them as They tread.
Reminds me of how there was a post on LessWrong some good decade ago, with a chilling premise: we somehow manage to get a safe, trustworthy, correct AI working, and as we fire it up and ask to tell us about our world, it starts talking about things we somehow can't perceive...