Absolutely! In fact, one is never more Jewish than when he or she believes in the Jewish Messiah! The one who addressed Jewish topics, before a Jewish audience, was Himself a Jew. Yet He was also the Messiah. God’s Word tells us He came first to His own (Romans 1:16) before enacting a plan to allow us as Gentiles to come to faith in the Jewish Messiah.
It is a beautiful story when the veil is lifted, enabling a Jewish person to know the Messiah. Here is one of many touching stories of that veil being lifted. Rejoice!