Yes, it is possible with Context Service SDK integration.
The on-prem CRM (or other systems of record) can store customer information and can be linked to Context Service Customer object using a unique key. So every time a customer calls in, IVR can lookup the customer to get the unique ID and all previous interactions (chats, emails, etc.) and use the Unique ID to get rest of the customer information from the CRM. Would that work?
By the way, we also plan to support a new security model with on-prem Key Management Server (KMS) around end of CY17.
You can read more about the end-to-end encryption capabilities of Context Service in the Context Service Security and Privacy White Paper.
Product Manager, Context Service