BIG-IP DNS Resource Record Types: Architecture, Design and Configuration

joeldavism thanks for the question and compliment! I must admit I had to go rewatch my own training to remember some things. I am giving you an answer based on my somewhat dated knowledge. 

You will be able to configure a static target CNAME as a pool member. It will NOT be eligible for health checking. The BIG-IP will simply return the CNAME to the client with no additional resolution. This is my recollection.

This leads to the obvious follow-up question, "Why?". It is for performance and some security reasons. A terminal pool member is an IP which is, as the name implies, the end. Once you have an IP, there is no more work to do.  If we allow an external pool member that is not an IP (terminal pool member) , and we allow health checks there are possible performance impacts. We could spend excessive resources chasing pool member health states against names we do not control. Think of CNAME loops in an external CNAME for example. 

I am also going to ask some colleagues to validate my answer because I am not working with BIG-IP DNS on a daily basis anymore. Hope this helps!