I am curious whether using both can be enabled on the site, and whether doing so will actually improve performance.
I currently use Boost and Cloudflare together on a medium sized site, I don't have any current performance figures to show you but there is a substantial improvement in performance and scalability by using the boost module with the cloudflare service. I don't use the cloudflare module itself as it only allows you to submit Spam reports & ban/whitelist IP addresses.
I use the boost module and have then setup my account on cloudflare.com to cache static assets like images etc Boost on its own does a great job of serving more pages faster. However as my site has a lot of static assets and that is primarily why i use the cloudflare service.