Its not clear what search you are referring to. Are you talking about after the screenpop has arrived and been accepted that you are wanting it to pull more info? PegaCA-CTI-Call.Startinteraction and ChannelServices-Interaction-Call.StartInteraction are the starting points . You may want to fire up tracer and see what is being executed.
There is no OOTB functionality to do what you are inquiring about. I would suggest you look at the Service Java calls that are available for the CTILINKevent service package for the JTAPI calls and see if you can leverage those to implement the functionality that you require.
Arun, As I mentioned previously there is nothing OOTB to perform such a task. You are going to have to see if you can leverage the pieces that are out of the box to do something to meet the requirements at hand. This may be as simple as transferring the call to the survey mechanism rather than hanging up. If that is the case search on the transfer activities. I would suggest doing an OOTB transfer and tracing it so you can understand the data involved and how it works.
Also you need to speak with your Avaya resources to understand what they are expecting.