Yes, Karaism is an interesting thing. Somehow, it could be very tempting to see it in relation with the Quran. But it seems appears after the 7th c. I think Dye thought about it.
I think the example of Karaism can be useful to show what kind of sects (secretive or not) could be formed in Late Antiquity. Out of what exactly originated Karaism, we can only guess. Just as we can only guess what the origins of proto-Islam were. But we do have an ealy text (Quran) and generals behaving in a novel way showing some people had the idea of merging Christian with Jewish material.
Yeez, I think your question of Jewish monasticism is relevant. Apparently there was quite some reticence towards monasticism although there are records of desert preachers (eg St John the Baptist) that fit quite well in the tradition later on developed in Christianity.
So we have both contrasting elements in the Quran: 1/ praising the monks 2/ Jewish style marriage promotion above all.
A sign to indeed look at a sect that was formed by intellectuals coming from both traditions?