A "gentile" is a non-Jew. So yes, it is self-evident that he converted as a gentile to Judaism.
I know this is proably way to in-depth to ever find a answer but here is some food for thought:
If all the Apostles were Jewish (Exception) Luke and there Jewish wives had children then by lineage they would be Jewish even if they believed Jesus Christ was Messiah this being the case how would you identify there geneaology?
Jew Gentile? no way to tell...I would find it interesting if someone had an answer to this puzzling question....