This is orthogonal to your point, but it is worth noting that the pronunciation of "αν και" is [an cε] and not [an kε]: notably, the velar [k] is palatalized to [c] before the front [ε]. Forgetting this assimilation is a common mistake by non-native speakers. It's a bit much to explain in one comment, but here are some resources:
(If you're using slashes phonemically and not phonetically, then your transcription is still correct—just pointing this out!)
That's true. I've seen that /k/ palatalized to /c/ in some greek words, like σκύλος (/ˈsci.lɔs/, not /ˈski.lɔs/). But to be honest, i always hear "/ˈski.lɔs/" or /an kε/. In Canary Islands, we aswell use the voiceless palatal stop "c" (for the word "muchacho" we say /mu'caco/ instead of the main spanish /mu'ʧaʧo/. But I can't find the similarity between the canarian /c/ and the greek /c/. I always hear a /k/ in these greek words :( Thanks for the links.
"Αν και" means "although". Αν on its own means "if". If you say τρώω αν δεν μαγειρεύω you say "i eat if i don't cook". Grammatically correct, completely another meaning. It's not just common, it's the way you must say it. You can always use "μολονότι" or "παρόλο που" for "although", also.