Some do, some do not.
It was mentioned by a developer once, that the Pokémon-world is better developed than our and most people are vegetarian. However, it can be seen, that some people eat meat, so I think you can say, that they eat Pokémon.
The following did not happen in the anime, but in the Pokémon-world
In the second generation of the Pokémon-Games (Gold, Silver, Crystal), Team Rocket sells tails of Slowpokes, which are a delicacy - That means that they're eaten, too.
Just to compare: In the anime, it's never shown, that Pokémon are killed, too - I think that's just because it's made for children ;).