As far as it being non-Abrahamic: it's in the same boat as Gnosticism in this regard. Yeah, it originally was not, but it readily adapted Abrahamic ideas and language.Would Manicheanism starting to some how grow count? It's non-Abrahamic, is organised in its structure and it is monotheistic.
It succeeding is a big maybe. It was always bigger in Persia and the Near East, and had little influence in the Roman Empire. Christianity succeeded in no small part because it spawned in the Roman sphere of influence, and had access to Rome's infrastructure to spread across Europe. To make Manichaeism succeed in the West in opposition to Christianity, you'd need to have Sassanian Persia become the locus of Western civilization. Which is virtually impossible by the time Manichaeism came to be, anyway, as the Sassanian Empire was very Iranian and the cultural legacy of Greece and Rome in Western Europe is hard to erase. Honestly, Manichaeism had its best success east of Iran, in Northern India and Tibet.