Stutterers experience varying degrees of fluency depending on their context. I rarely stutter when on my own, but it does happen sometimes. Same goes for singing, rapping, acting, talking to pets, children etc. We had a recent thread in here where someone asked about stuttering during dreaming, which I rarely do either, but it's not impossible. You'll find that what holds for your own stutter will not necessarily hold for another stutterer - there's a lot of difference possible, but of course, it's all the same general problem.