Was the Word, 2nd Person of Trinity, Jewish before he dispensed the Abrahamic covenant?

The New Covenant fulfills the Old Covenant, but they are both parts of one continuous plan for salvation. The Jews should have all become Christian, so to speak, because their religion pointed to the Messiah, and Christ was the Messiah. As a man, Christ did fulfill Jewish Law. He ate Kosher foods, was circised, ate the Pover, etc. It makes sense that the person who took the old Law to its completion would initially follow it.