there are plenty of different options for your scenarios depending on your requirements and needs.
Do you use just a plain TDM ACD from Avaya and you need the CVP as a network IVR to do queueing, you would consider deploying the CVP solution to avoid tromboning your calls and use a virtual transfer on the CVP side instead, you will have to implement some translation routes and the CVP as a network IVR, you will still have most likely your ILEC lines terminate at the ACD and a PRI connection between the ACD and the CVP controlled GW.
You have an IP extension on the Avaya side, you could interconnect the CVP and use it once again as a netwrok IVR, you should decide where it is the best to terminate the ILEC lines, wherever on the Avaya side or the Voice GW.
You have an IP Extension on the Avaya and are using SIP, you could deploy a CVP 4.0 with a CUBE server and talk SIP between the systems.
On top of all this, since you are already using CTI on the ICM side, you should be able to improve the overall call variable data population and update to/by the agents since it is a common interface.
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seeking help on some documentation on the integration explained and some case study available on the same.
hard to reply on such an old thread without knowing more of the specific, I don't know of anything being readily available to this level of detail. I would recommend reaching out to the partner help community or your Cisco sales rep if this is related to a deal going forward.