Ads are the main business model for the Web (some Web 2.0 sites use(d) freemium) but ads aren't the definition of Web 2.0.
Step 1) Provide a free service that will attract millions of users
Step 2) Track users and sell their attention to ad buyers.
Lots of internet businesses would have a hard time surviving without the ads business model.
It isn’t the definition but it sure seems like a huge integral part of it in reality.