Interesting hypothetical. I'm going to go with False.
First, we'd have to operate on the assumption that they don't know we're going to run, which I think is fair. If they do know, it's a clear false, as the defensive strategy becomes a lot easier. Also probably have to assume their offensive gameplan is unchanged, for example Ohio State's last two drives just bled the clock with the lead, whereas they'd be passing more if we were winning.
With Ohio State, we gifted them 7 points in the second half with a pick six, but they won by 12 so that didn't make all the difference. You also have to remember they got inside our 10 after our last drive (which ended in an interception) and then mercy kneeled. A lot of upset betters I'm sure considering the 12.5 point line. On a broader level, outside of Anderson's 93 yard run we were averaging 3.1 YPC. It's not like we ran the ball at will on them.
With Texas, only 1 second half interception resulted in points, and we lost by 15. Hard to say that was the reason. Another was a fumble, not a pick, resulted in a TD but even that was right around midfield. We did have a fairly good 4.4 YPC there so that might have gotten us some more points if we had avoided the turnovers, but remember that Robinson was our leading rusher that game. The RB's / WR's had less than 100 yards total, and averaged 3.4 YPC.
So I'd lean towards no for both, though Texas is more of a maybe.