I know that you can "hack" the regular buttons by running a network sniffer to catch the request and by not completing the setup it won't actually order anything. It would be up to you to then trigger something in C4. I don't think it would work natively, but if there is enough interest a product could be created (edit - I just saw the post above detailing a product in the works already).
Here's some good links on how others have made this work:
https://blog.cloudstitch.com/how-i-hacked-amazon-s-5-wifi-button-to-track-baby-data-794214b0bdd8
https://blog.cloudstitch.com/i-turned-my-baby-dash-button-hack-into-a-pager-for-toddlers-2cde1e59769a
https://www.networkworld.com/article/2991411/internet-of-things/hacking-amazons-dash-button.html
I personally would add a step on my home firewall to block the dash buttons from talking to the internet so you *really* can't accidentally order anything online. Good luck!
