Yes. Individual apps don't actually handle this. The Bluetooth device automatically sets up a messaging protocol with your phone and it will receive the messages completely separate from the SMS apps on your phone. The Bluetooth device acts in a similar way to any SMS app on your phone.
If they don't seem to be coming through, you could try forgetting and re-connecting the Bluetooth device, restarting the phone, or reinstalling Pulse SMS. All of these could wipe out any system level integrations. Pulse SMS does not have, and will not have, any configuration around Bluetooth devices. Individual apps do not manage this connection.
