In short, yes, they work and according to the feedback from people, for both happy customers and unhappy customers the anti snore mouthpieces do work in either reducing the snoring or even in some cases completely eliminating them.
What separates the happy and unhappy customers of anti snore mouth pieces is the fitting of the devices in the mouth. Some people bought the cheaper versions which need to be boiled, but they did not really read the instructions and some others were just more sensitive so they found it a very strange sensation to have the mouthpiece in their mouth. However, for the latter, you could get used to it over time as it solves a much bigger problem.
There are also various materials from which they are made. The cheaper ones naturally are made from less pleasant material. This also upsets some people who probably would not complain as much with the more premium versions which also do not require boiling like the snore no more mouthpiece.