People might respond, and many will help the system, because, to them, it’s the right thing to do.
However, people won’t be proactively assisting, and the assistance which will be offered, is the incidental kind, like when somebody happens upon the criminal or sees some wrongdoing occurring right in front of them. But, taking the extra step won’t be happening if rewards are just ruses to get the extra help the police departments need.
For reward-driven "snitches," the decision to "snitch" or not doesn't turn on whether the promise of reward is in fact sincere. It turns on whether or not "the snitch" believes the offer is genuine.
I don't think the presence of a reward drove the lady who contacted the cops about Dorner. She'd have called the cops, reward or no reward.