Can an Amalekite convert to Judaism? The Mechilta says no:
Rabbi Eliezer says: The Lord swore by His throne of glory: If a gentile comes to convert to Judaism, he will be accepted. But Amalek and his household will not be accepted. [Mechilta d'Rabbi Yishmael 17:16]
But the Talmud seems to say yes:
The descendants of the wicked Haman studied Torah in Bnei-Brak. [Gittin 57b].
Someone (who?) said that a descendant of Haman must have raped a Jewish woman, and she had sons who are therefore Jewish, and this is who the Talmud refers to.
Would they be Jewish? I know we are not able to recognize Amalekites today, but since a good five centuries or so passed between the injunction to wipe out Amalek and King Saul (almost) doing that, surely there were cases of men born of a Jewish woman and an Amalekite man.
Would they have been considered 100% Jewish back then (with no asterisk), or Amalekites?