It turns out that Robolectric's FakeHttpLayer only works with Apache's HttpClient, which is highly discouraged on versions greater than Froyo. Extracted from Robolectric's Google Group
That being said, the usage of HttpUrlConnection will cause you trouble. I'd try to use Android's implementation of HttpClient where possible, since Robolectric intercepts all calls to that library and lets you set up canned responses to your HTTP calls. We're looking at doing the same for HttpUrlConnection, though it's not clear when that'll happen.
Apart from that, a unit test should not need to mock the HTTP layer. My approach was wrong from the beginning.