I've implemented something similar on my apps, and I have to say, it works. Most users (including myself) simply won't give a good review unsolicited. If the request pops up and they like the app, it won't be that much of a nuisance (they can make it go away forever).

The trick is getting the timing right. Wait long enough that they've used it a few times and have actually had a chance to form an opinion. Otherwise it's just annoying.