I hope someone else can answer the question of the specific recorded beliefs of Crusaders in regards to demonic possession, but, in the meantime, I can answer with complete certainty the more general question of whether they believed.

Until relatively recently (and, actually, currently in the US), Christians, including during the Crusading era, have overwhelmingly accepted the presence of demons and the possibility of possession by them. After all, Jesus himself is described in the gospels as exorcising demons fairly regularly, even going so far as to speak with them and even make deals with them (as with the demons "Legion" and the herd of pigs). The main question was not whether or not demon possession was possible, since such questions were considered answered in Scripture, but how possession was possible and who could exorcise demons. To this day, the Catholic Church has rules related to the performance of exorcisms (you need to be an ordained priest with express permission from your bishop, iirc), and maintains the possibility of possession.

Source:

Brian P. Levack, The Devil Within: Possession and Exorcism in the Christian West.