Is it possible to add remote device to BIG-IQ?

Indeed, my previous response was a bit lacking. In K36398804 it is said: 

F5 recommends that you set up and manage the BIG-IQ HA configuration in a low network latency environment. While F5 does not provide a firm latency guideline, it is the general acceptable practice to keep latency between elements in a BIG-IQ HA configuration within 75ms. This includes links between BIG-IQ Centralized Management (CM), BIG-IQ Data Collection Devices (DCD), and BIG-IP devices.

While this latency is perfectly possible to achieve, even via internet, I do hope that's not what you're thinking about. I'm not even sure NAT is supported, and I've never tried any NAT configuration between BIG-IP and BIG-IQ.

/Mike