I * think * this native formula does what you want:
Code:
=IF(SUMPRODUCT(($A$2:$A$11=$I11:$Z11)*($F$2:$F$11<TODAY())),"At Risk","On Time")
It "looks up" the IDs listed in I11:Z11, finds them in column A and then counts how many of them have a finish date later than today. If any of them do, then it returns "At Risk".
Perhaps I misunderstood though.