In Type-0 HD, you have the ability to enable or disable support characters (so far, they seem to just be fixed level special NPCs you can't control). They take the place of your party members temporarily, and fight alongside you. As they do things, you earn SPP, a special currency. However, at the end of a mission you're graded on Time, Phantoma, and Casualities. Do support character deaths count towards casualities? My own experience seems inconsistent so far.
Through my own testing, it looks like the answer is Yes, any support characters that fall in battle are counted against you in the casualities stat at the end of the mission.
My testing: I did the final mission of chapter 6. This ends with an "unwinnable" fight. As a result, the boss likes to hit VERY hard. I benched everyone besides my leader so they wouldn't die (but support characters still appear; I verified that none of my characters had died before this point). One of the support characters appeared and then immediately died. My results screen listed 1 casualty.