I think a noon game would make Ohio State more disinterested. A night game, even as the visiting team, is somewhat more energized and I think that is likely to carry over to them as well. At noon, the game feels much more 'small time' and could lull them to sleep.
I think the opposite is true. They are in distant land hundreds of miles from home. OSU will most likely get here Friday and have to wait all day Saturday to play on someone else's field. They have all day for anxiety and other bad feelings to build up inside. How you would feel if you had to wait all day in a hotel to play, uh, Rutgers? Plus, look at the big B1G night games we played at home: Penn State (almost won) Michigan (won) Michigan State (could've won).
May the odds ever be in our favor!