I mean, if there are no paid ads on the site it won't track any.
That said, I don't expect this to be the end state of their user tracking. They could expand their system to track the kinds of ads we get here on HN too. Maybe eventually start ups will be able to pay Mozilla to track how many firefox users use their web apps after seeing a "Show HN" post or even just after seeing mentions of a product in comments. Right now it's hard to track the success of astroturf campaigns, but when a web browser is working for advertisers instead of being a user agent it becomes possible.