I think you can accomplish something close to your scenario...
First you'd have to setup a recording policy in Admin->Quality.
In Architect you'd have to use the "Enable Participant Recording" action.
Play a prompt to ask them to speak their address and email.
Call a data action and send the ANI and the ConversationId to your web service.
Play the thank you message and disconnect.
The web service will have to use the ConversationId that it received to pull the recording using the Recordings API, when the recording is available after the call completes (note this can take a few minutes). Then your web service can store the ANI and the audio file on the file server for someone to listen to it.
The only difference in that approach is that your web service has to obtain the recording using the API instead of the audio file being sent via the data action.