Yes, the chance to get money is always a good reason to do something. It doesn't matter what it is. If people know that they can do one simple thing and there's a chance to win money, more than likely that one simple thing will be done for their chance at money. That's how the world works.
Sweden is ahead of the curve in many ways, but the latest of these may be their "Speed Camera Lottery," where safe drivers are eligible to be rewarded with a lottery prize. This is a great way for people to want to drive more carefully: they might not know if they will be rewarded or not, but it's the idea of the reward that will get them to reconsider reckless driving habits.
It is the dream of many to win a lottery, to have financial worries gone and live comfortably. The idea of another chance to achieve that dream just by driving the speed limit, without having to make an additional investment aside obeying traffic laws, is a hugely appealing idea and would encourage lots of people to drive more carefully.
I think this a great idea. People just need some sort of incentive to obey this law. If I knew I was eligible to win a lot of money if I obeyed the speed limit, and I didn't know when my speed was being tested, I would always make sure that my speed is below the actual limit.