Fragments like this used specifically can be good English, IMO. I would like to see it in context, like the whole paragraph.
first and last parts are 'good english' grammar... middle two are fragments, not sentences... some fragments can work, even thought they're not technically 'good english'... can't tell if they work here, without seeing it in context...
I agree with the above posters. They could work depending on context, though I feel the third part (second fragment) causes some problems with "while." The purpose or meaning of the second part (first fragment) escapes me--this could be due to lack of context. It may be simpler for you to say, "He was. Then he wasn't."
I would say good English is anything that works regardless of what grammar teachers say. But good English is in the eye of the beholder. Without context, the above looks choppy, but with context, it could be used to good effect.
the problem I have with it is that I keep noticing the full stops more then I can read into what you are trying to convey and for this reason I am not so keen on it. in my world there is nothing better then words that float freely as oppose say stop/break say/break. that is me.
