Like Surbhi mentioned, you could create some custom software to send telemetry to the cloud via email. However, the Edge Agent module on the device will need to connect to Azure IoT Hub. It can't do that through email. Without the agent, you can't receive deployments. And so, it won't be able to function as an Edge device, without losing functionality. Basically, you will need to treat the device as an offline device.
You will also lose the ability of sending device to cloud messages through the Edge Hub, and lose the ability to receive or send module twin updates. You will also be building custom modules to send emails, instead of using normal telemetry messages, and when you're done building these modules, you can't download them from your customer's location. You will need to bring them somewhere that allows connecting to IoT Hub to update them. Every time you make a software update, you will need to sync the device to receive updates.
Convincing your customer that setting up an AMQP connection is safer than using email should be easier and less costly. Don't forget that although AMQP/MQTT are bi-directional protocols, the device initiates it. There is never an incoming connection from the cloud. Also, how are your edge devices going to receive OS updates? Surely not by email?