For reference, the first time I asked was here: http://physics.stackexchange.com/questions/2188/does-electri... (7 years ago - time does fly). There is a bunch of discussion there (also going into at what point a water analogy breaks down), and I'm not sure they agree with each other. I mean, another way of looking at it: you can encode n bits by charging (or not charging) capacitors. Does a series of capacitors encoding '0' have a lower mass than a series encoding '255'?
So yeah I don't really understand, still not after all those years. It's probably (in part) because I have not formulated one single yes/no question that is unambiguous or does not need any interpretation to be answered. Or maybe I'm just stupid.
Look, you can just look at how this stuff works. Electrons move randomly, and when there's a current they move on average in a certain direction because the electric field leans that way. That's it. See my link I pasted above, it describes what happens when a current is flowing.
A capacitor encoding '0' will have the same number of electrons as when it encodes '1' because that's the way capacitors work. You can read about it at https://en.m.wikipedia.org/wiki/Capacitor
I think a decent analogy is a pneumatic air power distribution system. Air particles move randomly in the pipe, but if the air is flowing, they tend to pass through the customer in a given direction and get work done. Alternating current is akin to switching the direction of air pressure twice a day, from (say) 1.5 atm to 0.5 atm.