I think there is a story in ?? about a Ger Amoleki who Dovid Hamelech killed. There is some sort of ?????? ??????? if I remember correctly if an Amoleki can become a ??, and they bring a ???? from this story that he can become a ??, but will retain his status of Amoleki.
According to that, a ?? who from ???? will be ?????? to kill himself, because he will be ????? on ????? ????.
I dont know if a mitzvass eseh of michias amolek would be able to be docheh a chiyuv misah bidei shomayim (suicide).
You also should consider that for jews there is a concept of shchitah so he may have been mikayem the mitzvah as soon as he chops off his own head, or the idea of shchitah may only apply to animals but for people “death” is when the heart stops beating.
Yekke: That Shittah in the Tannaim, which seems to be accepted by Rashi and Tosfos, has been roundly rejected by almost all other Rishonim and Achronim and isn’t even used as a Snif L’hakel to be Mattir an Agunah. Everyone knows that the world-accepted P’sak is that being Jewish or not goes after the mother.
The idea that a child of a Jewish mother is always Jewish was not accepted by all.
R’ Akiva Eiger (in Yoreh Deah), and the Maharit Algazi and Maharshal (Yevamos 16) all say that such a child requires a form of geirus/tevilah.