Hi LZ1,
1) Do you have a link to any page at GoDaddy that describes the free hosting plan? I want to see what they offer with that and maybe it will give me a clue as to what to try.
2) It would be fairly trivial to set up a server to ignore calls to a file that WP needs to run. If GoDaddy is adamant about not letting you do it, there's very little we can do and your client may need to learn the meaning of "the ISP won't allow it"
3) What you could do is setup a remotely hosted WordPress (
http://wordpress.com/) and then just include it in a iframe on the clients domain...