Nope the ASM does not relay/generate CLID (and I wish mine did).
Interestingly, while the Norstar itself does not support Caller-ID-Call-Waiting, if you happen to be on the cordless phone served by the ASM at the time a CLID-CW call comes in, that CLID signalling will pass through the Norstar/ASM to the cordless. So it gets what the rest of the system can not, but only that.