I established the bluetooth connection between the devices. However, the speed download/upload still stays low (< 1 MB/s) between the devices while it should be much higher with Bluetooth 4.0 in both devices: Macbook Air Mid-2013 (adapter) and Samsung Galaxy S4. BTsync should use local network to share data between the devices in the sharing.
I contacted the BTsync support about the issue
Unfortunately we don't support bluetooth so Sync establishes connection through LAN or internet, if there are firewalls and NATs it can be established through relay server. But Sync uses the best possible connection for synchronization. We'll don't plan supporting bluetooth in nearest future but we'll think about it.
So it is completely technically possible to support file sharing in the local network by Bluetooth.
How can you enable BTsync file sharing by bluetooth in OS X with Android?