CUE 2.1.1 (out soon) will have a CLI command 'show ccn call...' which can show you all calls currently in the system. I'm not sure that that will help you too much though.
You are correct that when all ports are busy you will get at SIP message:
SIP/2.0 480 Temporarily Unavailable
The easiest way to determine if this is what happened is to session into the CUE CLI, then issue a command such as follows:
cue-3660-41a> show trace buff long | include exceed
3065 12/27 01:29:44.930 ACCN SIPS 0 CTIPG_ROUTE_EVENT:CTI Port Group route event: Route Session=null,Route Address=11000,Failure reason=The Trigger has exceeded its max number of concurrent sessions,Exception=null