The short answer is no. Big Sisters are grown Little Sisters; they won't play the role of a Big Daddy.
Big Sisters are created in a similar way to Big Daddies, however, most Big Sisters use a giant needle as a Melee Weapon, which in turn can be used to extract ADAM.
Big Daddies are there to ensure an individual Little Sister is able to extract ADAM without being harvested by Splicers. A Big Sisters' role is to make sure that all of Raptures ADAM is circulating properly, and that none is stolen. They are more efficient at Little Sisters' roles, since they are able to extract more ADAM more quickly, and they can find more ADAM and protect themselves as they carry it. Big Sisters will protect Little Sisters if they find any who are being harmed or robbed of ADAM, but you won't find them guarding over Little Sisters as Big Daddies do.