yeah you can, just click on add a site and enter your blog address and add meta tag to your blog, thats it!
I am using my blogger blog with Google Webmasters and it is working fine. Google is indexing my web pages everyday.
Yes, Of course you can add any type of blog in GWT. If you are on self host, it's recommended to use the file upload method to verify. If you are not on a self host, you have the option to use meta tag to verify.