Can some stars not emit any energy in the visible spectrum?
Light that is not light


That's meaningless.  All light is electromagnetic radiation.  A finite part of the infinitely large range of the electromagnetic spectrum is visible light.  So you should talk about EM radiation and to discuss the visible spectrum just say visible spectrum.

Stars emit lots of energy at frequencies that are outside the visible range.


  Dark Matter


Dark matter does not mean that it's just not radiating in the visible part of the spectrum.  It means it's not radiating in any part of the EM spectrum much.  If dark matter exists (and that's not certain) it won't interact with most matter much at all.

If dark matter were in star-like objects, it sounds very unlikely that there would not be any EM radiation as a result of the interactions that would result in a star-like object.  We'd detect it if it were there.  So I don't think that's likely.