...yeah, probably. You'll get your holdouts and weirdos, but with nothing with which to buy ammunition, food, and shelter, the overwhelming majority of your soldiers will just go home and try to accomplish their religious goals some other way. The guy who runs the training camp has bills to pay. The construction crew for seige equipment and combat engineering think of the money they should be making as a contracted business instead of humping their ass for free. Without a salary, commanders don't feel like their lives are getting better having gone through the ranks with all their experience so how long do you think they'll last before sending their resumes around? Fortifications cost money. Roads, animal logistics, communications, that all costs money. If you've had any success at all, mayors and chieftains are going to start asking who the hell put you in charge and really the only answer to that is "I sign your paychecks" or they'll just straight up replace you with someone who can. You could kidnap all of these people and try to get some Mongolian style slave army going, but then you need to pay the kidnappers and the people who'll enforce that - police states are not cheap to run.
Like, seriously, name a Muslim army that worked for bupkis. Who are you even talking about? Even the prophet Muhammad himself had the backing of the Medinan government; he had to convince them that his religious credentials were legit, but without their rubber stamp none of this gets off the ground.