Web-Bluetooth with Background Functionality?

Imagine the following scenario:

1. Customer places order for product on third-party website
2. Third-party website sends notification to server with details
3. Background process on android tablet waits for server push notification
4. Process pushes data to bluetooth device which then prints a label.

Is it feasible to have something running in the background on an android device that:

1. Maintains a stable connection that automatically reconnects to a bluetooth device
2. Accepts server push notifications and then sends commands to the bluetooth device
3. Is fairly fault tolerant

At the time of writing, Web Bluetooth doesn't support background mode.

This isn't a near term goal according to https://github.com/WebBluetoothCG/web-bluetooth/issues/422.