To add in a little more, according to Geoff himself a while back, he told me that, when the contestant picked the box with the big check (on both runs), the producers told him how much time he had to use before revealing the check. This would not only allow him to build up the suspense and keep the flow of the show even, but also to let the crew get the balloons ready for dropping!
And, just to reiterate another point, yes, Emile handed Geoff the little slip with the number on it at the end of the show.
Hope this helps!
Anthony