A similar strategy which I read about somewhere is to ask people if they they are happy with the product. If not, ask them if they could tell you why not and how you might improve in their eyes. If they are happy, ask them for the favour of rating the app. To me this seems like a pretty covert way to keep the unhappy customers from submitting bad reviews while at the same time gathering feedback. If you show them that you appreciate their feedback, you may even turn a bad experience into a good one.
Nope, haven’t tried it, just read about it. But seems like it might work.