You should think of it more using the transaction cost based approach. Government money is artificially scarce, therefore it has high transaction costs, therefore it hinders trade instead of facilitating it.
The purpose of the scrip is to issue a money that isn't artificially scarce so it's transaction costs are low. In this way you don't get a stimulus, rather you are getting rid of dead weight loss. A guy pulling a rickshaw is naturally going to fall behind someone who can walk without baggage. The point isn't to make the runner faster or stimulate his performance via some sort of doping.