Their direct work output contributes to a functioning democracy, but does so indirectly by providing material goods and services, which I refer to by the shorthand "economic reasons". We don't train nurses and carpenters because their training directly supports democracy; we train them because we want to live inside and be cared for when needed, and these things are incidentally good for any society, democratic or otherwise.

They may of course contribute as individuals, too, but their training is not required for them to do so.