I believe it does - I use Cloudflare with my blog and every file, including *.html files, appears to be served by them.

The documentation and marketing on cloudflare.com is a bit misleading on this. Unless you do something unusual and potentially fragile with their page rules, it does not cache HTML: https://support.cloudflare.com/entries/22094188--Does-CloudF... It will hit your server for every page request.

(In fact it only caches certain static files as determined by their file extension. It does not seem to pay much attention to Content-Type of Cache headers. Ugh.)