It looks like the folks at Sparrow have started to enable push notifications for a handful of users. Perhaps this is a part of a larger rollout?
YouTube personality Duncan33303 has reported that push notifications are now working on his 1.1 installation of Sparrow, as have others.
According to a blog post on Sparrow's website, the push update was supposed to be available in the next released of Sparrow, that being version 1.2. It appears, however, that the developers of the highly popular Mail app alternative may have included code in the 1.1 update to make push notifications work without the need for Apple's approval...