Free checkout works on my site with 1,7, with only the paypal module enabled (I have the other COD and Bank wire installed, but they are not configured so I assume that they are not enabled).
I did have a problem when I removed the obligation to tick "Terms and Conditions" checkbox...the button greyed out, so I thought I'd mention it here in case anyone else is searching for the same resolution.
Apparently you can't have a free order without that checkbox.