Is it technically possible to listen to Bluetooth signals with the AD936x ? The issue is, that BT does 1600 frequency hops/sec in 80MHz Bandwidth, using 79 carriers of 1MHz each, or 40 carriers 2MHz. While AD936x has 56Mhz max. BW.
AD9361 does not support more than 56MHz bandwidth. The internal analog filter bandwidth is limited to 56MHz and any signal outside that range will be heavily attenuated. You can use AD9371 for your use case which supports 100MHz BW.