No, AdSense is a business model in which there is a simple javascript widget interface. The model is money in exchange for advertising across billions(?) of websites. A startup is created and launched when there is a business model that uses the widget. Otherwise its a programming exercise. Any reasonable programmer can create a program in <10 hours, but unless there is a business model it is not a startup.
A good example being YouTube? Or Google (before adwords)? Twitter? Delicious? Reddit (before advertising)? If you build something people want to use, monetizing it is always something that you can pull off.
I would say that a business model has to exist eventually-- and a startup ought to have a few in mind. But I don't think an active business model is required to be labeled as a "startup".
