Which IP does my F5 use to authenticate against Active Directory?

The basic answer is "it depends". What I mean by this is that the F5 will use whatever IP is appropriate, based upon its routing table. If you have a default route that uses a self-IP to contact the gateway, it should use that. If you don't have a default route which would use your self-IP, then it should use the default route assigned to the management interface.

You could check to see what the system thinks by running the following in the bash shell:

ip route get 

From there it will tell you which gateway the connection would use.

Some more documentation on how the BIG-IP handles management routing (if you prefer the AD traffic use the management interface) is here: https://support.f5.com/kb/en-us/solutions/public/13000/200/sol13284.html