Sprint doesn't care if it's rooted. They just charge you the deductible if they know is rooted and there is nothing broken (like if speaker is out, that's a manufacturer defect). If it's crack or broken then yes you still pay the deductible. The key to uprooting is to replace the phone for free under a manufacturer defect.
As to refurbished phones. Many are new* phones. By new, I mean sprint can't resell a phone that has been sold by their system. Example, you buy a new gs3 ring it out and right after you change your mind. Sprint can't sell that phone even if is not open. So those phones go to warehouse and then they go to insurance.
Of course that's not always the case. Refurbish could be a returned phone that someone used for less than 14 days. If the phone has any imperfections then the casing gets replaced or screen gets changed, etc.
I had 3 refurbished evo 4Gs and never had issues with them. I had them replaced cuz I broke them lol
Also I'm a fan of refurbished stuff. One of my computers is a refurbished, I got a tv like that too... Heck my blender is refurbished. All looked brand new out of the box. Worked the same as "new" items and costed 45-50% less.
^_^
