Will they test me for a personality disorder?

usually they do, but with out knowing where you are from or what you have told them about your symptoms I can not say for sure, but if you signed up for a "study" than it seems like they would since like you said ED is usually co-morbid with other disorders. Best of luck to you, and it is better to know what is wrong than not to know since there are treatment options out there for most illnesses of the mental variety.