Orpingtons tend to have a more docile personality than many of the other popular breeds, and some are not good about standing up for themselves which can lead to bullying. But it really depends on the individual birds involved too. I have one orpington (from a breeder, not a hatchery), two ameraucanas (also from a breeder, one is my rooster), two speckled sussex (from a hatchery), an easter egger (from a hatchery), and a silver laced wyandotte (also from a hatchery). In my mixed flock, my orpington is towards the top of the pecking order if not top hen and I've actually seen her step in and break up fights. She even puts my rooster in place on occasion. She's very laid back, but she doesn't let the other birds walk all over her.
My bet is that if you are getting orpingtons along with the other breeds in a hatchery order you will most likely not have any problems with the orps getting bullied. They may be at the bottom of the pecking order, or they may be at the top, but more often than not chicks that are raised together will get along just fine into adult hood, even if they are different breeds.