Do you mean through the call? Or do you mean on the client machine from the agent desktop. From the call, not that I know of, unless there is a CUCM feature that allows it.
So to clarify you are saying, we could have a gadget button to ask the call to be transfered to an ivr/RP recording.
Or should the agent transfer manually? It may be easier to have a button...
This is all theoretical based off of what I know about Finesse and UCCX, but yes. You can have a button on a gadget and have the RP number hardcoded. The only thing is if the agent has more than one call, you will need to determine which call gets transferred.