TextSecure for Android is only distributed via the Play Store. So I built it myself only to notice that Google Play Services are required for chat. I think depending on proprietary / data gathering apps is the wrong approach for an open source privacy app. It actually makes me sad. There was an issue about "This requires Google Play" on GitHub [0] which was closed by moxie with "TextSecure only requires GSF for data…
whatsapp and telegram also use google play services for background notifications. There is no other reliable way to ensure that messages are always delivered on both iOS (push notifications) and Android (Google Cloud Messaging).
Apps just don't get enough API access to do this on their own in a totally reliable way and even if they did, the overhead of multiple applications keeping multiple connections open (and the radio active) would cause a lot more drain on the battery.
Neither TextSecure not Signal use the platform provided notification features for unencrypted data though, so your messages are still safe.