Yes. ποτήρι is derived from πίνω; I drink. That in itself comes from the proto-Indoeuropean 'peh', according to Wiktionary.
Pottery comes from pot, which comes from the proto-German 'puttaz', which is also derived from proto-Indoeuropean - but 'budn', a type of vessel.
So I don't think there's any directly shared roots even though they sound almost exactly the same.
Having said that, there are tons of Greek words which are cognate with English words - you'll come across plenty in this course.