I'm not familar with godaddy sites specifically but you can certainly include the FileMaker PHP API within your site folder and have it talk back to the Web Publishing Engine located elsewhere - I do this all the time.
This blog article on the Goya site covers the same territory but with reference to a linux server:
but should explain the process. You just put the PHP API files in your site and "include" them, making sure you have the correct relative path.
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Thanks - I must just be having problems with my realive path.