You're expressing that as a yes or no situation, but it isn't. It's a relative speed of energy input and output, and there's a crossover point.
Cranking the engine will take energy out of the battery very fast. The alternator will be putting it back in, but slower. So there will be some amount of time where it gets back in as much energy as it initially lost from starting the engine. I don't know how much time that is, but it's likely not within just 1 or 2 minutes. Also, that's not just a fixed rate from the alternator. Its speed of energy regeneration is tied to how fast it spins, from the engine RPMs. So that's why it's frequently recommended to drive a car around some, rather than just letting it sit running at idle, if the goal is to recharge the battery some.