There are two main ways to do call recording, either using the phone's built in bridge (BIB) or using a network SPAN to capture the RTP stream. Typically I've seen verint using the BIB of the phone to send the audio streams to the recording server and CTI/JTAPI is used as well for call information, on demand recording, between verint and CUCM. If you're not using SPAN for capturing the audio stream I don't think you can record soft clients like CIPC, CUPC, CUCILYNC because they do not have built in bridges and I don't think the software will duplicate the audio streams to send to the recorder.
This is an older guide but still might be true:
http://www.cisco.com/en/US/docs/voice_ip_comm/uc_system/UC6.0.1/features_apps/CMmonrec.html
Call monitoring in Unified Communications Manager Release 6.0(1) is supported by all 3rd-generation phones (Cisco Unified IP Phone 7911G, 7931G, ,7941G, 7941G-GE, 7961G, 7961G-GE, 7970G, and 7971G-GE models).
Obviously newer phones are also supported now like 89XX/99XX, which are not in this list since they have a BIB (DSPs in the phone).