IP Communicator is not tested with IPCC Express 3.x and hence not supported. Hope the new IP Communicator will be supported in the upcoming IPCC Express 4.0 release.
For more details do touch base with product management team email@example.com.
From a previous email thread:
We are planning to support the new IP Communicator in the upcoming IPCC Express 4.0 release. In the currently shipping IPCC Express 3.1 and 3.5 you can use the Cisco IP Softphone instead.
Please touch base with product management team (firstname.lastname@example.org) for roadmap details
I can second this. We have a customer actively using CallManager 4.0(2a), IPCCX 3.5(1) and IP Communicator 1.1(2) with the Cisco Agent Desktop software in the field with good results.
From a CTI or XML applications perspective, if it's supported on 7970, it ought to work on IP Communicator. I'm sure the IPCBU folks would like to officially certify this before they take TAC calls on it, which I can respect.