NO that is not what Dr Hahn is getting at! The Eucharistic Chalice is the Third Cup of the Passover not the 4th, please see Brant Pitre- Jesus and the Jewish Roots of the Eucharist: Unlocking the Secrets of the Last Supper as Dr Hahns Lectures assume you have some basic knowledge of the traditions and Theology behind what he is discussing, whereas Dr. Pitre doesn’t have this assertion in his book.
Christ did drink the Eucharistic Chalice, as the third cup (the Chalice of his Blood) is before the singing of the Great Hillal if you follow Dr Hahn’s thinking. Scripture does not explicitly state whether he did or didn’t but as to complete the Passover meal 4 cups would have to be consumed (only 3 of which are in the Last Supper, through close examination, and eisegesis using Jewish Traditions of the day, plus some inter-gospel comparisons and St Pauls Epistles) and a 4th Cup (hyssop branch) being consumed on the Cross to complete the meal and the sacrifice.
If you want me to go into this argument in depth please respond, as you have misunderstood Dr Hahn’s argument (although to be fair, Dr Hahn does not explain himself to well, considering he is speaking to Theologians and Biblical scholars generally of Post-graduate level in his lectures so he makes assumptions as to your background knowledge) which Dr. Brant Pitre also makes, but a lot clearer.