Hmm... that is also an interesting theory. Come to think of it, Doflamingo bought Sugar from somewhere instead of recruiting her, which implies she might not be as loyal to him as the rest of his family. Trebol might have been put by her side to make sure she doesn't betray Doflamingo. This also means she was probably sold as a slave, probably at Doflamingo's very own slave shop. And if she is indeed a slave then it is possible she has some connection to Koala, as they are very likely the same age.