I think, yes, that the "CloudFlare-issued" means you have to use a CloudFlare subdomain... But again I did not test. Even if it works, it's still twice as expensive as GAE, doesn't seem to cache the HTML files (as per above comment)...
BTW: they use certificates with multiple SANs, so many different domains in the same certificate (and without SNI). This allows to terminate SSL on a single box for many different domains/customers. If you look at certificates details, you will see many unrelated domains in the SAN list.