I don't know who "they" are. I don't speak for Southern Baptists, so I don't know what any church would necessarily do. In the most recent version of the Baptist Faith & Message of the SBC, they specifically call out that "the office of pastor is limited to men as qualified by Scripture."
Now they are not using the extrabiblical terminology of "senior pastor", and their statement can be interpreted a number of ways. The most straightforward way is that there should not be any women who serve as shepherds - whatever that means. The problem is that in every church I have known - including some who are downright extreme about women not having official leadership roles, there are women who shepherd other members of the body without the title. Often - especially in small churches - the true pastor (the one that the congregation looks to on a longterm and consistent basis) is a woman who has served the congregation faithfully for decades, not the young man that will be there for 20 months and move on.
And I don't know what you mean by "elder." Women serve on committees throughout Baptist life. They are often elders in that sense. Moreover, mature women in the congregation are often looked to as a source of knowledge and guidance.
In many churches, deacons serve as a board of elders, but that is not necessarily biblical either.