Net energy produced requires a net reaction; even if an ‘AC Battery’ could be instantiated you’d still need a net reaction to produce energy.
Imagine a ball rolling up and down a hill. Our hill has no friction, and our atmosphere provides no resistance.
The energy available is the mass of the ball * the height of the hill * the acceleration due to gravity. The mass of the ball isn’t changing, and gravity isn’t changing, so the best we can do is get the ball up the other side of the valley.
The moment we try to extract any energy from the rolling ball to do something else, it’s ability to get up the other side of the hill is diminished. So even if it rolls back, a bit, eventually the ball will stop.
Thus, the AC scenario you invoke only works in the case that
- something else can store the energy released and
- all of the energy stored goes back into charging the battery
Even assuming zero losses, you could not use the system as described to produce net power.
As for “AC batteries”, well, there are certainly ways to invert DC to AC, but they don’t enable the reaction as described above nor in the paper.