Not in every situation. ESC is no use if your tyres are not touching the road.. for example in the last couple of post where the member chose CFE for ESC component due to his past experience of spinning his Myvi because of aquaplaning. ESC is not going to help him in an aquaplaning situation since the tyres are no longer touching the road. Both the car and the driver are just passengers in a four wheel boat spinning on top of the water.

ESC helps by applying brakes and power to assist in the stability. Anything that needs additional driver steering input to correct like a sudden oversteer cannot be corrected by ESC.

To spin, you need to lose traction to all 4 wheels, otherwise how are you going to spin? Once you lose traction on the wheels, you no longer have directional control. ESC does not work if you don't have directional control anymore.

1 wheel hitting the puddle will not do much harm. Only when all 4 wheels hit the water and lifts the car completely off the road which then I consider as aquaplaning and ESC will not help.

Once the car starts spinning, nothing much can be done by ESC/traction control to stop it as all 4 wheels no longer have traction on the road. Driver input by steering in the correct direction can help stop the spin faster by trying to align the wheels to the spin to regain control.

ABS works when you are travelling in a straight line by providing you control without locking up the wheels. Once you start spinning, the tyres no longer have the traction to give you control.