No, it's not. The Host: header goes under HTTPS aswell, your browser directly connects to the IP-address and initiates a SSL-handshake first - after that, it submits a regular HTTP-request.
Er, sorry. Thanks for correcting me on that. Not even the domain is exposed.
Here's more info on it:
"If you look in a network sniffer, like Network Monitor, at the same request you would just see the encrypted data going backwards and forwards. No URLs, headers or content is visible in the packet trace":
- http://blog.httpwatch.com/2009/02/20/how-secure-are-query-strings-over-https/