No, Elijah, a Jew remains a Jew no matter what religion he or she belongs to, even if he or she is practicing a religion whose tenets run counter to Judaism. The problem with Jesus was not that he was considered to be the Messiah or that he performed miracles - many rabbis at his time were said to be the Messiah and performed miracles - so Jesus is not that special in that regard. The problem arose because the early Church claimed he was both the Messiah and God. In the Jewish concept, the idea that a human being could be God is considered to be the height of idolatry, suitable more for pagans.
10 arrested at Israeli Arab protest in Ramle (Haaretz)
from the article: 'He'd say kaddish for his mother'