The Nine Houses being what they are, it wouldn’t surprise me if the Cohort had their recruits’ genetic profiles on file just as a matter of record.
So wouldn’t it be fun if Gideon had escaped the Ninth, and two weeks later Harrow gets a missive from the Cohort saying that the new recruit has tripped a red flag in the genetic database. She has no definite matches for any relatives going back at least 300 years. Would the Reverend Mother or her appointed representative be so kind as to please confirm that Gideon Nav is a real person who is known to the Ninth House?