No they couldn't and Baptists don't have parishes. Most churches don't even send a representative to the national convention and I doubt half the regular attending members could name the head of the SBC, or even the director of their local association. SBC churches just don't work that way.
So what do they do if you get this?
"Hi, I'm Pastor Joe from the First Southern Baptist Church of Louville. I'm here for the National Convention. Over at my church, we preach that Jesus was just a very nice guy and not divine, that the Bible was written by ordinary people and there's nothing special about it, and we actively marry gay couples and celebrate abortion! Last Sunday we had a Muslim preach to my flock that you can accept Muhammad is your savior and still be a good Christian! So where do I take my seat so I can lobby for the entire SBC to take these positions?"