Yes and no. A mid third quarter 'oh shit the clock is running out' when Gilbride is calling the plays, can't be on Eli, at least not entirely. If it's in a hurry up offense, then sure, but it seems to me that Eli only calls the plays on hurry up.
But, and I could be wrong, I remember them mostly happening in situations like mid third quarter on a 2nd and 6; where you don't expect it at all.