This doesn't answer the question.
The app is productive in the chrome web store (as mentioned in my question) and still doesn't show productive ads.
As much as I appreciate your answer here I'm a little surprised that you just reference a question on SO that doesn't have an answer (as indicated by my comment to that question).
Shouldn't the AdMob team have an interest in showing ads in chrome os apps? Don't you wanna to increase the traffic for your network?