I have a Kobo Touch and have accessed the Content Server with the built in web browser. I don't use it often as I have to charge the Kobo anyway so I usually use a usb cable - but it is definitely possible to set up.
From Calibre's help pages:
"calibre has a Content Server that exports the books in calibre as a web page. You can turn it on under Preferences->Network->Sharing over the net. Then just point the web browser on your device to the computer running the Content Server and you will be able to browse your book collection. For example, if the computer running the server has IP address 63.45.128.5, in the browser, you would type:
http://63.45.128.5:8080 Some devices, like the Kindle (1/2/DX), do not allow you to access port 8080 (the default port on which the content server runs. In that case, change the port in the calibre Preferences to 80. (On some operating systems, you may not be able to run the server on a port number less than 1024 because of security settings. In this case the simplest solution is to adjust your router to forward requests on port 80 to port 8080)."