Wow! That's a blast from the past: CAD Agent chat integrated with Presence.
I'm nearly positive you cannot do what you're thinking, and the Agent is actually supposed to not use both at the same time. They would only use Jabber to setup new contacts and lists, but then close it, and use CAD Chat 100% of the time to conduct business.
You might be missing the point of integrating CAD/CSD with Presence for SMEs. For example, the whole point of including IM&P functionality is so that CSD/CAD users are not limited to sending contact details or conducting call control actions within the Call Center user realm, but rather, can include company SMEs who do not belong to the Call Center.
Else, why even use CAD/CSD chat at all, and just use Jabber 100%?
https://www.cisco.com/c/en/us/td/docs/voice_ip_comm/cust_contact/contact_center/crs/express_10_0/design/guide/UCCX_BK_DF6A995E_00_design-guide/UCCX_BK_DF6A995E_00_design-guide_chapter_010.html