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I have a client with a couple of XOOPS sites on godaddy. The sites are fairly low volume, and mail works fine using the PHP mail option. The 'from address' is set to a godaddy hosted mail address (or alias) in all cases.
The client has one of the virtual server packages, not just a simple hosting plan, so there could be differences between offerings.
I would try godaddy support, as it should work.