I'm not sure I follow this argument. People who think there are no such things as "souls" think human beings are living creatures, and to be a living creature is not just to be "electricity and cells" in the sense that I, for example, am not a dead body over here plus a generator over there.

Now, as you note, a living person who is in a coma also, presumably, feels nothing. Someone who thinks people do not have souls should, however, say that this is because a certain part of the person's brain is not active, or is not active in the right kind of way. Its not being active means, to be sure, that there is no the right kind of electrical activity in that part of the person's brain. But this is not to say that it is the electricity that would have feeling, if only it were there. It means that the person does not feel anything because that kind of electrical activity is not then present.

Indeed, there is a classic challenge here to the conception of people as embodied souls: If people are embodied souls, why should certain kinds of brain damage cause them not to feel anything? What does brain damage have to do with what happens in the person's soul? Are we making a huge mistake by operating on people we've sedated?