The network architecture behind BBM, especially with the addition of video and voice, has been sort of a black box. We learned a bit about it when corporate admins had to open up the firewall for voice and video calls. Now with Android and iOS support we learn that the BBM connection works over SIP through a TLS (encryption) transport. Thanks to a new Knowledge base article we now know that it makes a SIP connection over TLS to global.uci.blackberry.com over port 443.
If you are having issues with the requests on your carrier you should check out the details here with BlackBerry. It seems like some carriers are blocking SIP to block VoIP apps.