Well I certainly don't see the Romans embracing Christianity.
seconded, the Romaioi were Hellenistic Polytheists, with local Latin names for Greek Gods.
They may conquer Yehuda, but unlike Kart-Hadast after conquering Egypt from the Ptolemaioi and taking their homeland of Tsur-Ea, the Romaioi has absolutely no reasons to try to suppress the Yehudan Religion and worship of Yahweh, while the Karthadastim, whose Pantheon centered on Baal-Melqart, has every reasons to supress "The Cult of Yahweh" because they are very hostile to any kind of Baal Worshippers.
Which absolutely backfired when governor Adonibal Kanelyon ordered the death of Yahwehist Preacher, Joshua bar Joseph by crucifixion. so close with the Baalist mob murders of Yahwehist High Priest, Joseph ben Caiaphas, which galvanized the two previously separate sub-sects of the Yahweh Cult.
Combination of Yehudan Rebellion AND the spread of Cult of Joshua ha Massiach toward the Hellenistic Kingdoms (hence the term Christians, for Joshua bar Joseph would be known as Iesous Christos in Greek), sealed the fall of Karthadastim.
The Combined Yehudan Revolts, and attack from Hellenistic Christians ended up breaking Karthadast domination in Mediterranea, paving the way to the dual Hegemony of Pergamon and Syrakousai.
With Romaioi, or even (obviously pre-conversion) Hellenes controlling Syria and supressing Yehudan religion, there will be no quick widespread of the Cult of Christos.