IF you only have the godaddy domain registration, but hosted elsewhere, you should not have any issues...with that said, it can have a cascading effect on everything when one domain server site as big as that one goes down.
Namecheap for my domain registration (always have)
My server is thru hosted thru wiredtree.
However, we also have our own nameservers.
IF the web servers at Namecheap are hacked, it does not affect the domains registered there. But it can cascade to them.
Go daddy gave me a free month of Dec but instead of charging me $1 I noticed it was $5.99. Not a lot but still a lie. I don't like that!
I moved all of my forums from Godaddy hosting to another server after this fiasco. Lesson learned.