Yes, belief in free will has complete impact on whether or not they have it. Free will vs. determinism, both are personal truths, personal perceptions of the world. If one person believes in free will, that changes whether or not he chooses his actions, but does not affect others. Free will isn't something that can be proven. If a person chooses (heheh) to believe that they have no choice in their life, then 1) the very act of choosing to believe this will be "decided", 2) they will not ever consciously choose anything again, because in their mind, everything is decided.