Many SLPs stutter! If you look at organizations like the American Institute of Stuttering, at least two of their clinicians are people who stutter. Also, if you're familiar with "StutterTalk" podcasts (http://stuttertalk.com), a solid chunk of their hosts are SLPs who stutter. I agree that you'd have some unique insights into the area that may make you more accessible to clients (and maybe more appealing to hiring managers). I also know SLPs who stutter who went into the profession intending to work in the area of fluency, but then fell in love with a different area of practice (i.e. swallowing disorders, preschool language, etc.) and have had a lot of success. If it's something that interests you - go for it!