Would it be possible to have a push message triggered when in proximity to an iBeacon? Currently all BLE apps I have experience with seem to only allow messaging within the app while it is the focus app in the device.
anyone have experience with this type of set up?
As far as I understand you're asking about the notifications triggered when the app is in the background.
You can read about it here:
I hope this answers your question.
Do you mean push or local messages? Both shall not be confused. Only Apple can send push messages to your device when your server asks Apple's server to do so.
BLE devices of any kind, like Estimote or a heartbeat sensor do not send local or push notifications. What happens is: Your app detect beacons and then it asks iOS to show you a local notification.
Regarding background mode, see the link mentioned by Ola and I have put a comment there.