Depends on the school, depends on the adcoms. You cannot get a definitive response here due to the variable nature of the answer (as is the case for many questions here on SDN).
Your best bet is to mention these ties in your application and discuss how they influenced you to apply to the school in question. It certainly won't guarantee that you'll be treated like an IS resident, or that you'll even be considered to be any different from the remainder of the OOS applicants. But, the admissions game is sometimes about using anything and everything to your advantage, and in this case, the possibility does exist that these ties may help you. Worst-case scenario, mentioning the ties does not help you at all.
Think of it this way: mentioning the ties and potentially having a leg-up is far better than not mentioning them at all and being guaranteed no advantage!
I think it depends on how close you are to such family members. I know I barely ever talk to my mom's brother's family, and I'm just now getting in touch with people on my dad's side of the family, so saying that I want to move to ND because my aunt and cousins live up there wouldn't mean a whole lot...