Hey Opp,
I have wondered about the same thing. I have a half-sister who is (actually...she just became a U.S. citizen) a foreign national and was wondering if that would affect the adjudication.
As far as your foreign national family members knowing, when I first got my COE I called someone at the CIA to see if it was okay if I told my half-sister. The guy I talked to said he called the security department and they said it was okay to tell her (she has lived in the U.S. essentially her whole life and was in the process of applying for citizenship, so maybe that's why they gave it the okay). That being said, depending on your circumstances, I think it could be okay that your family members know about your future employment.
And as far as the security clearance goes, this is a little more unclear. I know the CIA explicitly says that spouses must be U.S. citizens, but they hardly mention other immediate family members. This website has a list of DOD security clearance cases that were initially rejected then appealed:
http://www.defenselink.mil/dodgc/doha/industrial/. There are a number of rejected cases due to family members being foreign nationals. Also, I know the State Department recommends that people seeking TS/SCI clearances generally need to have all immediate family members (parents, siblings, etc.) be U.S. citizens.
Of course, each department and agency has slightly different guidelines and standards, but I would think that if other government agencies take issue with foreign national family members, that issue would at least raise red flags with the CIA.
So, I guess what I am saying is that I don’t know what affect it will have. I don’t think it's an automatic denial, but I do think it could ultimately matter, depending on the circumstances in your case.