Hi! My name is ***** ***** I am an independent web expert paired with you through JustAnswer.com. It is my pleasure to assist you today.
GoDaddy's customer support agents told you the truth! Google/Bing/et al. do not take into account any of your back end hosting information; that is to say that the sites do not index nor rank you based on which server (or OS) you are hosted on, what platform you are running on, etc. In fact, you would be able to (and many do) completely switch web hosts at any time with no effect to your search rankings so long as your actual site -- and the SEO work you've there incorporated -- remain the same.
In this case, you're not going so far as even a hosting change -- merely a platform upgrade. Rest assured that the hard work you've done to increase your search visibility will remain unaffected.
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