What is the difference between static electricity and electricity from a battery/power plant?

Static electricity

An object holding a static charge has an electric potential. If it touches an object with different electric potential a current will pass until the potentials are equalized. One can choose the zero potential. I think the most sensible way is to say that an object with the same amount of protons and electrons has zero electric potential.

Electricity from a battery

The electricity doesn’t flow unless we connect + and – poles of the same battery. Current won’t flow between + pole of battery #1 and -pole of battery #2 unless we connect also -pole #1 to +pole #2.

My hypothesis is that a battery pole has a small static charge that can discharge into a neutrally charged object (but the current pulse is too short to be measured by a regular meter). If we connect the two poles of the battery the electrons are returned and the small static charge on the poles of the battery is continuously regenerated.

1. Is my hypothesis about the battery correct?

2. Would it be possible to create a significant static charge by connecting say 10 000 AA batteries in series? We could make a straight line from the batteries and place conductive sphere on each end to accumulate charge. Assuming a single AA battery has a voltage of 1.5 V and length of 5cm, the voltage between the ends of the chain would be 15kV on a distance of 500m. Could we carry a charge from one end to the other using a conductive sphere? Would the effective voltage of the battery depend on the size (capacity) of the transfer sphere? (because the charge would get depleted and only regenerate as we bring it to the other pole)