I don't have experience with nmap so unfortunately I cannot help out with that tool. BIG-IP does block ports by default. The problem with connecting to the iControl portal over HTTPS is that in Java you need to have the server certificates installed in the client truststore to allow a trusted connection to the server. Also, you would need the authentication credentials for each machine you are connecting to. You could determine if a machine was serving up https, but you couldn't know if it was a BIG-IP.
One solution that is possible is to scan the network for servers listening on ports 683 (CORBA IIOP) and 684 (CORBA IIOP+SSL). These are the ports that BIG-IP exposes the CORBA interface on. IIOP+SSL (684) is not likely to be supported on other products and would likely indicate it being a BIG-IP so I would look for this one first.
Good luck, and let usknow how it goes. Also, if you get some code working for this, we'd appreciate snippets you could contribute to this site.
-Joe
Nimbostratus