The reason Sparrow lacks push is related to which notification API's Apple allows app developers to use, but the developer promises a fix in a blog post today about the new Sparrow version 1.1 update:
What’s up on Push?
Thanks to your amazing support, we feel confident that Apple might revise its position on the Push API. We’ll submit a first version of Sparrow 1.2 including it. This might delay Sparrow 1.2 validation but we’re already working with some partners to include Push in future versions of Sparrow without needing Apple clearance.
Push is coming. With or without Apple.