Amazon Connect-Based Outbound Calling, Remote System Control, and Disaster Recovery Without Internet Dependency

To facilitate secure outbound calling, remote system control, and robust disaster recovery, without relying on end-user internet connectivity, a solution can be architected using Amazon Connect’s telephony infrastructure in conjunction with AWS Lambda for backend orchestration.

https://docs.aws.amazon.com/connect/latest/adminguide/disaster-recovery-resiliency.html

https://docs.aws.amazon.com/connect/latest/adminguide/outbound-communications.html

Your question is a bid broad, so I'll try to break it down.

1. Can Connect be used as a disaster recovery system to make outbound calls? Yes.
2. Can the functionality of placing outbound calls be turned on and off via a phone call? Yes.
3. Is it secure? Yes.

Now, how you do it is a whole other ball of wax, but get familiar with contact flows and Lambdas and that will get you more than half way there.

david