I think it could be plenty successful, just not as a form of Christianity. It would just be an adaption of the Jewish God into the Roman pantheon (he was identified with Caelus and sometimes Bacchus) with Jesus deified as his son. That gives some weird theological questions since it makes Jesus Saturn's half-brother and Jupiter's uncle.
Wasn’t there also a brief period of time before the full Christianization of Scandinavia when people would worship Jesus alongside the Norse gods? IIRC there are some archaeological finds whose status as Mjolnirs or crosses is ambiguous, perhaps even deliberately; this plus the Hellenistic identification of Yahweh with Caelus and the Manichaean utilization of Jesus as a prophet might provide some jumping point. I agree that such a religion would not be Christian, more of a pagan faith with elements borrowed/syncretized from Christianity.
And depending on how you define Judaism, at one point it did acknowledge the existence of other gods, just they were not worthy of worship. This seems apparent from passages in Jewish scripture.
Maybe one could end up with a functionally (if not doctrinally) polytheistic sect if the sect in question is willing to play loose with the definition of “worship”. I’m imagining something like pagan-descended folk practices and beliefs, except somewhat more explicit in doctrinally incorporating the existence and appeasement of other beings, even if they don’t refer to them as gods (after all, things like leaving porridge out for the nisse and certain practices relating to Mary and the saints are basically a form of offering or sacrifice even if doctrinally recognizing them as worship would be heretical). Basically like early forms of Christianity, except the folk religion is actually incorporated into the sect’s canon (so Celtic Christianity would end up considering the Sidhe as a canonical part of their doctrines, for example). Or maybe the sect resembles OTL Christianity, but pagan deities are more explicitly equated with Christian ones to the point that their worshippers are linguistically pagan but ideologically syncretic (so a Norse Christian might worship the trinity of Odin, Balder, and… idk, Hermod? while a Roman Christian might worship the same deities but with the different names/myths/canon of Caelus, Bacchus, and Proserpina - obviously the actual deities identified with different angels/demons/Trinity facets/saints would probably be different since I’m just thinking of equivalents off the top of my head). This would probably necessitate a less united Church to begin with and either diverge at or butterfly Constantine, since if Christianity becomes the state religion it becomes easier for the Church to enforce orthodoxy (see what happened to Arianism in Germania).