Here is my response to my own question.
AMD XConnect Techonoly does not officially support external Thunderbolt 2 enclosures but it does work on my particular setup.
OS = Windows 8.1 64 bit.
AMD Crimson ReLive Version = 17.9.1.
CPU = i7-4790K
GPU = R9 Nano (Fury X)
Motherboard = ASUS Z97 Deluxe Dual with NFC and Wireless.
RAM = 32 GB Crucial Ballistix Tactical LP.
Hard Drive = Srasgate 1TB SSHD.
External Thunderbolt 2 encosure.
GPU = R9 Nano Fury X.
It works, however I have been unable to turn Crossfire on. I do not believe that is supported with AMD Crimson ReLive XConnect technology, although it would be good, if Crossfire were supported.
Reasons: Running the R9 Nano in the external Thunderbolt enclosure provides better Airflow around the card rather than having the R9 Nano fitted inside the PC Case on the Third PCIe_16 Slot on the Motherboard in the case where I run 3 R9 Nanos in Crossfire Mode.
I will add a few screenshots regarding what I see with AMD Crimson ReLive 17.9.1 below illustrating the External Thunderbolt 2 enclosure connection.