Arcing only happens when the voltage is sufficient to cross the distance, depending on the dielectric coefficient of the medium. To answer the question, yes, it can happen but as I understand your original question, you're not concerned with large voltages, you're asking about current at a very small level, which is how I have been addressing my comments.

If two batteries are connected and one has been depleted, they shouldn't be lead-acid because the byproduct of repeated or rapid discharge prevent the plates from recharging as well as virgin lead and acid. To your question about a difference that's too small, I don't think so- everything I was taught and have read says that as long as a potential difference exists, even if it's one electron, it wants to move. Take away the net charge and you'll have no current. However, if you make/break contact or move the wires/bodies, the charge can change because of Triboelectric effect. This can be heard in audio cables with a center conductor that can move inside of the dielectric when walking on or handling the cable.

If you allow the batteries to remain connected, then no, you can't easily measure current but you could connect a small resistor in series and use an extremely sensitive device to measure the voltage drop across the resistor. However, at the level of charge in the one or two electron range, it's unlikely that we have anything outside of a major lab to check this.