If you're talking about the type of spiritual battle I outline
here, then I suppose I understand what you're talking about. But the concept barely applies to any battle involving the Witch-King since he has so little power on the spiritual plane. If the battle was one of wills (spiritual power), as you say, it would unquestionably be no contest at all. Which is why I am sure the Witch-King would have avoided such a confrontation, just as he avoided Glorfindel.
That said, I don't see why the Balrog would be hostile towards the Witch-King, since he would most likely recognize who he represents.