If the Kingdom of Judea survives as a coherent part of the Empire under the Antipatrid dynasty, given that dynasty's Roman citizenship, longstanding status as friends and allies of the Roman people, and so on, and then you get a member of said dynasty who is educated in Greece or Italy, serves in the Roman army and then gets to a position where he can proclaim himself Emperor in the normal way, I can see it happening. But any such Antipatrid would be very unlikely to be a religious Jew - few of the Antipatrids were especially so (and, as they were Edomites/Idumaeans forcibly converted to Judaism, originally, some might not even count them as Jewish ethnically).
It would mostly require, as I said, a coherent, longstanding Antipatrid government, unlike the rather piecemeal and non-continuous series of Antipatrid-ruled ethnarchies, proconsulates and provinces that made up the true history of that dynasty. Which pretty much means you need, first, for Herod Antipatrides to formulate a coherent succession, almost necessarily including one of his sons (as opposed to killing a number of his sons, which constantly destabilized the succession - combined with his Stalinesque paranoia of overthrow) succeeding unhindered by the Romans, which would require a strengthened position compared to OTL, and for the sociopolitical and religious situation of 1st-1st century Judea to stabilize. The former is difficult; the latter seems practically ASB.
Honestly, though, I can't see any other family in any other situation producing an at least arguably Jewish Emperor, particularly in the case of a PoD after the Diaspora, with identifiable Jews - even the Hellenized - suffering a probably inescapable level of "otherness" due to that nigh-universal inscription, IVDAEA CAPTA. An emperor of limited Jewish heritage isn't impossible, but such a person would be so far displaced by integration into Greek or Roman culture and religion that it would be effectively meaningless IMO.