What do you mean by free websites? You can get AdSense approval for any website as long as it is abiding the guidelines.
I think you can give it a try.After all, the final deceision is made by Google.You will never know the result unless you try.
Yes Definitely You can USE Free Website To Open New Adsense Account, Blogger is also free many people applying from blogger. and is our website is match with adsense criteria than you will definitely get approval as well..
Yes of course, I applied adsense using their own blogger -I created a subdomain with them and made a personal blog. Its about 1-2 weeks old when I applied for an account. I was verified after 2 days, which made me happy. I was not aware that lots of people are having big problem with the application.