The Blank Center For Stuttering in Texas talks about this a lot - how stuttering can lead us to miss out on or not pay enough attention to other aspects of communication (such as the example you brought up) because we're so focused, whether consciously or subconsciously, on not stuttering. Focusing on those other aspects of communication (eye contact, listening, turn taking, etc.) that we're usually capable of improving without the extreme struggle that we're used to when we try to improve our fluency can be really empowering, because others notice that we're not worried about our stuttering and can capably communicate in ways that are important to us.