We don’t know for sure what the devil knew about Christ’s identity during the temptations in the desert, and the authors of your study Bible should not have been definitive in their speculations. It is possible that Satan was trying to determine Christ’s identity; that is certainly a valid speculation. But it remains speculation. We just don’t know for certain.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.