That's assuming you have a public folder. We do because we've been using Dropbox for a long time but apparently if you created your account recently you won't have a public folder.
AFAIK only the primary public folder on Dropbox will let you host web pages. Any other public links that you create will not show the actual web page but will appear as a link to download the html file. In this case there are some third party applications that will let you host web sites on your dropbox.
Another option would to use something like curl to upload the files to an ftp server.
And yet another option would be to use the VC TcpPlugin and the "simple web server". This works fine, except that the current version of the plugin does not support css files. I'm pretty sure this can be fixed though, if there is any interest.
Once set up, all of these options could be made "automatic" requiring only a VC macro be executed to do the updates and copy / upload in order to refresh your html to show your latest commands.