It is not a scenario I have seen in my games. When I shuttle US troops through north Africa, I sometimes manage to take India but that is mainly with a USSR supported US stack.
But what was Japan doing? Even though Germany is a bit defensive against the Soviets, Japan should be able to either hold India, or realize it can't pull back to FIC and retake India and maybe also Persia in the next round(depending on number of transports position of fleet etc.).
Combining both the US North Africa rush and the India Crush is probably a good way to execute this strat (both Soviets and Americans converging on Persia) but the question is how Japan acts.
If you openly try such a maneuver it will become the elephant on the room for the Axis - they'll be ready to react because they'll be monitoring the progress of the US across North Africa and it's fairly easy for Japan to stop the US advance and prepare for the Soviet thrust on India by focusing on that route.
But usually Japan advances through the 3 routes (Yakut, Sinkiang and India), so its ground forces will usually be split. Also, Japan can have a tendency to send its fleets and planes to Africa/Europe/etc., away from India, contributing even more for a dispersion of its forces.
If so, then the move of crushing India can work. Germany defensive stack in Eastern Europe, Japan dispersed and divided through Sinkiang/Yakut/India/elsewhere. Japan builds IC, Soviet stack on Caucasus moves south. Watch Axis react!