Not long ago, a friend asked me if connecting via SSL makes him anonymous, for example, to blog anonymously.
Here i will assume that for the sake of the example you are blogging from a country where the government does not allow free political speech and you don't want anyone to know that you even visited that website.
Before you begin, you will need to register a domain name and add privacy to it before you checkout, if you checkout with the domain name and add privacy to it later, you will more than likely have your domain name whois data public, defeating the purpose, If you plan to do something illegal, Domains By Proxy (The Anonymous registration service) will probably drop the service and reveal your name.
The short answer is NO, the long answer is YES if you can take care of some other aspects.
There are also other ways (Encrypted but not as Web SSL) that allow you to encrypt all your browsing and DNS, that way is to tunnel into a shell account described here.
To begin with, before you can connect to a website, your browser will be performing a DNS lookup, Most people use there ISPs resolver for that lookup, so you are in effect asking your ISP what is the address of example.com, and therefore, your ISP knows you have visited this website
a simple sollution is a hosts file, on windows this is commonly at (Make sure it works by changing the address of other websites and you are sure it works), also be sure to include both www and no-www
When you request the connection, although no name is transmitted in plain text, you are connecting to the IP of the website, something that your ISP will find in there log files.
The sollution is to have your website installed on an IP address that has another website that uses SSL heavily, the other website should not be yours, and preferably, not someone who knows you, People would be connecting to that particular website, and you would simply sneak with them through there SSL connection. Your browser would display a warning that the security certificate belongs to apopularwebsite.com and you will need to allow the connection manually by adding an exception, but to your ISP it looks like you are visiting apopularwebsite.com and not example.com, they know that zero or more of those connecting to that website is visiting example.com but they have no way of telling who.
Although the website is on an HTTPS connection, some elements like images of the website may refer to HTTP pages on your website, Surely your browser will display the mixed content problem, sometimes the browser will prompt you before fetching them, and other browsers would fetch them and then tell you that there is mixed content (SSL and non-SSL), if the case is the second, you have already been exposed, so it is best to make sure the content on the other website has no elements that are hosted on HTTP !
Your host will always have a log file of who accessed what, and unfortunatly, there is no way around this one, If you trust your host, go ahead and focus on the previous three points, if you do not, then don't even bother.