I don't see why not. Lots of poets invent words - that's how English develops! The word "chortle" was invented by Lewis Carroll in Jabberwocky and that's now in common usage. Just because it's not a word doesn't mean it can't be understood quite easily! As for another word...depends on the context. Numb? Heartless? Cold? Empty?
Perhaps being feelingless is the best feeling one can ever feel. But if one can feel feelingless, then one is not actually feelingless, is he? So in conclusion, no one can ever feel feelingless, because to feel feelingless is to feel something, and to feel something is not to feel feelingless.