Overview
It is possible to cache the HTML of a WordPress site at Cloudflare's Edge using a feature known as "Bypass Cache on Cookie". This can dramatically improve the speed of your website and reduce server load; in cases where the HTML is cached, Cloudflare will not need to make a roundtrip to your web server. In order to utilize this feature, please see the article: Caching Static HTML with WordPress/WooCommerce.
Cloudflare is able to proxy HTTP traffic of any website, including WordPress sites with third-party performance plugins installed, however, please note that these plugins are installed at your own risk.