Wow, surprising. Whether or not it would work depends on whether the running apache process (and thus the PHP running uc_file) has RW permissions on the folder. I'm not that familiar with GoDaddy's Apache configuration to say for sure, but I think the owner set automatically via FTP process is the same owner when the apache process serves files from your hosting space. In which case, it would work. I guess you can test it out to see.

As far as the permissions, I believe 744 will be fine for the file directory if you wish to read/write to it.