Nope.
I've talked to people who've never been premium, never paid a single red cent to NP, cheat and are still playing.
I've talked to people who've bought hundreds of dollars of NC/Premium and they got iced.
My main was iced about two weeks ago, it was premium. I don't think they really care (although they should!)
Here's what I think:
Edit: Found this, so I guess my last ideas is null and void!