yep you need to go through greenlight and you don't get any expense beside greenlight fee. I'm not sure about this, but i'm pretty sure there is something written about it on the greenlight faq.
edit:
I have a free game – can I still submit it to Steam Greenlight?
Yes, you can submit your free game to Steam Greenlight. Note that once your game has been Greenlit and you are preparing for release, any in-game transactions or subscriptions available to Steam customers must be purchasable only by the Steam Wallet.
I think that the reason not a lot of people are doing this is that it's time consuming. making the free game, greenlight process, bug free release. If you don't do it well it will just tarnish your brand .
Greenlight process (number of positive votes) might differ from regular projects.
Dodge Roll also did that with
Fork Parker's Holiday Profit Hike and their next game isn't free.