Don’t know but if so, she must recuse herself. At first blush, it would appear that her job would include issues brought against the Office of the President or were of such importance that the Office of the President would want to participate via a briefs to the Supremes. However, in this unique case, she has a financial interest in the outcome (her salary and other emoluments) since if O is not a natural born citizen, then his appointments are illegal and voided ab initio.
Good point!