Hello Jonathan,
Thank you for reaching out.
What you want to achieve is Full site delivery via CDN. Meaning not only the static files are served from the CDN, but HTML also.
This is possible to achieve, but not the way you mentioned.
For FSD CDN, I would recommend using Stackpath CDN as a provider. Also, note that the FSD CDN feature in W3 Total Cache is only available for Pro users.
Thanks!