A new article at Gamasutra argues that yes, they do, and in fact are necessary to a free-to-play game's monetary success.
"If you are going straight after this demographic at the expense of a wider audience, you will struggle if you want to be a worldwide success," the introduction explains, "especially if you want to be seen as real AAA-title rather than, say, a casual game. This is due to the fundamental fact that free-to-play works best at scale."
The article lists three primary reasons why non-paying customers help a game. The first is that they bring new users via word of mouth, and a certain percentage of those new users will become paying customers. The second is that freeloaders can show appreciation in other ways, such as cross-promotion between games and generating community content. Finally, this segment of players can be the targets of advertising, which is in itself a huge revenue generator.