Hey @golestane, it seems like your basic ask is "Can GoDaddy support hosting websites built using WordPress?" and the answer is "Absolutely YES!"
Glad that you are inquiring because choosing a hosting provider is one of the most important decisions when building your web presense. I saw a great Garage article called Choosing web hosting services: 7 developer requirements that might be worth a read. If you are new to hosting, WordPress or websites in general have a look at the GoDaddy Managed WordPress hosting product, it's great for easing into the world of WordPress. Hope that helps?
roy darling *my posts seem a lot shorter in my head
We actually do support the mod_rewrite module in all of our Linux based hosting plans. As for the PHP and MySQL versions you've indicated, those are actually the recommended versions and not the minimum required versions to use WordPress.
All of our hosting plans currently support the minimum requirements for WordPress to function. As for the recommended settings, you're correct in that we do not yet have these available. However, I know our developers have been working continuously on hardware upgrades that will also allow for a future update to support these versions of PHP and MySQL.