Does my stutter make me sound like I have an accent different then my own?

Does my stutter make me sound like I have an accent different then my own? First time poster and I would rate my stutter mild-moderate. I was born and raised in the US but my parents are from Eastern Europe. I believe I have an American accent but I've had a decent amount of people ask me where my accent is from. I notice when I listen to a recording of myself I defiantly have a really deep eastern European accent but when I listen to myself without it its American. I was talking to my mom who has a mild stutter and she thinks people are probably confusing my stutter for an accent. I get people asking me where my accent is from both when I stutter and don't. Just wondering if anyone else has experienced this.