No, the connector doesn't have any option to allow complete desktop control. By design, Windows Home Server is simple and easy to use for non-technical folks. The only supported interface for modifying and tweaking your server is the Windows Home Server console; anything that would require full desktop access is unsupported. It's also potentially dangerous; if you don't have a good bit of familiarity with servers in general, and with the differences between a regular Windows Server 2003 server and Windows Home Server in particular, there are familiar tools and techniques that can cause a variety of issues, right up to data loss and even the need to wipe the server and start from scratch. A good rule of thumb is that if you don't see it in the console, it's certainly unsupported, and may have a potential to cause some harm.
That said, you can use remote desktop to connect to your server. You will need to use the Administrator account and the password you created for the console when you set up your server. By default, the firewall on the server is configured to allow connections only from the local subnet; I would recommend against changing this, as there is a known "man in the middle" attack that Remote Desktop is vulnerable to that would make it potentially dangerous to access your server this way over the internet.
You should take a look at the documentation available through the console and connector Help facilities, and on the Microsoft site
here. That will probably answer a lot of questions you might have.
I'm not on the WHS team, I just post a lot. :)
