If you don't put enough in to get you out of the red in one go, it will not register, or if it does, it will add a very modest number of miles.
I have been playing this game for most of last week. When I knew my R was imminent, I was putting in £3 to £6 a day in from empty. The needle never moved. On the day I drove to Durham, I worked out that I must've had nigh-on a gallon beyond zero miles left (due to the non-reading), it still made for a tense drive to the dealership, doing 18 miles beyond zero reading.