If I set a file to chmod 777 in general webspace area, can anyone access and alter that file?
If you mean can any joe bloggs come along who doesn't have password access to your site and edit the file and hack your site easier, then no.
Sometimes, for example when installing forum software, and depending on the hosts configuration, you have to set some files to chmod 777. Again, it doesn't mean that someone can come along and wreck your forum by changing those files.