Of course you can do it. But you need to start about the architecture differently. BLE is not your old style bluetooth where you pair two devices and the only those devices can talk together.
Have your modules implement a peripheral role, exposing the data as GATT attributes/characteristics. Then have the PC, tablet, what have you implement the central role and periodically poll your modules - i.e. connect to them, read the data they need from the GATT characteristics and/or write any feedback data.
You can even have your modules simply broadcast the data blindly (without connection) and the PC/tablet/phone connects to them only when it needs to send some data to the devices. That's often how the various fitness/exercise machines are implemented.
Assuming that you have your network credentials setup correctly (devices are bonded together or broadcasting data freely), this will work just fine as long as the modules keep advertising (so that they are discoverable and connectable).
However, I think you need to make it clear for yourself which version of Bluetooth are you trying to use. At first you talk about BLE but then about pairing and headphones - which is Bluetooth Classic (there is no audio profile for BLE yet, AFAIK). A totally different beast that is unable to do what you want and uses a completely different hardware (e.g. the popular Nordic nRF52 modules don't support Bluetooth Classic at all, only BLE).
Nordic has a ton of excellent documentation on BLE, I suggest that you start there to learn how the protocol even works and what you can do with it. And also what it takes to use it - implementing a BLE device using one of the Nordic modules is not for the faint of heart. Even if you avoid the legacy proprietary SoftDevice and use Zephyr RTOS instead, the learning curve is STEEP!