That's almost exactly what I would say. These people willingly signed the dotted line to do it and knew it would probably involve things they would not want to do.
Correction: Things they would prefer not to do but have willingly consented to doing because they are getting paid for it.
I think the soldier comparison is apt. You sign up. The organization feeds, clothes, houses, & cares for you. You get paid. In exchange, you do what they say, which is what you agreed to do when you signed up. If you try to opt out, that is called desertion and they'll throw you in jail.
Because they have consented to everything that is being done, the original personalities are not slaves. You could argue that the Dolls have rights separate from their original personalities. Caroline is not a slave but Echo might be. For the most part, this is not an issue because the Dolls have no self awareness or desire for self determination. But what about a long running self aware imprint like Dr. Saunders? What if she decides that she does not want to cede her body back to its original owner?
Also, suppose a Doll's original personality imprint was lost or destroyed. Who does the body belong to then?