As I understand it, Crone has backed away from some of the views put forward in that book. Nevertheless, it remains useful for its excellent bibliography, which was the first serious Western effort to collect a lot of the primary source material. In particular, that book gathered Syriac chronicles for information on Islam's origins, which had not been grouped together previously.
I am currently studying classical Arabic and reading medieval tafseer (Koranic commentary). The more I learn about Islam, the more I have no doubt that it has its origins in some heretical Christian sect in Arabia - possibly something like the Collyridians mentioned by Epiphanius of Salamis, a group that believed that the Holy Trinity was the Father, Mary and Jesus - the Holy Spirit being identical with the Archangel Gabriel. This horrific misunderstanding seems to be what Muhammad himself believed. The Koran, in relating the stories of Jesus, Mary, Zechariah, John the Baptist, etc., seems to have been influenced by various apocryphal works, especially the Armenian and Arabic Gospels of the Infancy, focusing on fabulous extra-biblical tales.
There are certain doctrines and legends in Islam that to me make it clear that it had its origins as a Christian heresy - the Virgin Birth of Jesus being a Koranic example, but there is also a legend that Satan "kicks" everyone while they are still in the womb - everyone, including Muhammad, except Jesus and Mary (and of course Adam, who was created from the earth). Is this some corruption of the doctrine of the Immaculate Conception?
I'd always be careful of such 'historicism' in apologetics, since these same lines of 'logic' (albeit misguided) can and are applied to attack Christendom, from arguing pagan roots of Christian theology and even liturgy, to the 'competing Christianities' of Bart Ehrman, to the 'refutation of the canon' many believe the Qumran texts to be (since they predate the Masoretic texts as well as the Codex Vaticanus Graecus 1209 and Codex Sinaiticus).