Hard to find data without the help of Wiki and http://www.sports-reference.com. But in the last four national championship games that featured OSU, who do you got?
2002 - No 3rd string QB saw the field/threw a pass. Jim Otis and Matt Trombitas were RS sophomore and freshmen, but I don't think they ever played. I believe Justin Zwick and Troy Smith were red shirtted and wouldn't be on the depth chart, but Zwick was #3 in 2003.
2006 - Todd Boekman (soph). I think Todd got a bad rap and was a capable QB as he was older. Imagine him being terrorized by the Florida DEs.
2007 - Antonio Henton. Or possibly Bauserman (both true freshmen). Wow.
2014 - King Dolodale (RS Soph)
For funzies:
The 1996 team full of NFL talent, finished #2: Tom Hoying. I'm assuming that was Bobby's little bro?
1998, finished #2 - Steve Bellisari. My earliest Buckeye memories are David Boston's catch vs ASU and Bellisari's DUI which led the way for King Dolokrenzel to slay his homestate Michigan