No there shouldn't be an issue with emails sent to godaddy email addresses. They may have different spam filters... do they show in a spam folder on the godaddy email box?
Your friends over here at WebAssist! These Dreamweaver extensions will assist you in building unlimited, custom websites.
These out-of-the-box solutions provide you proven, tested applications that can be up and running now. Build a store, a gallery, or a web-based email solution.