It's not valid as a deductive argument, but it is Bayesian evidence in favour of naturalism. Also, the details of the observed effects of brain damage provide even more for naturalism rather than nonnaturalism.
It's not valid as a deductive argument, but it is Bayesian evidence
The "not a logical disproof" defense can be used against more or less all arguments drawing on empirical science. It would be more charitable to assume Richard means something like "the probability of brain damage by region delicately affecting particular parts of information processing is reasonably high given belief in souls." Although that still looks quite wrong. The "radio" analogy would not predict a speech center, or other patterns of brain damage and impairment that look like interfering with computation, not transmission.
No plot spoilers here, just wanted to flag a bit of poor reasoning that shows up in Chapter 39:
This is a surprisingly common fallacy. Just because X depends on Y, it doesn't follow that X depends on nothing but Y. A phenomenon may involve more than just its most obvious failure point.
To illustrate: Suppose I'm trapped in a box, and my only way to communicate with the outside world is via radio communication. Someone on the other end argues that I don't really exist -- "There's no person beyond the radio receiver, for if there was then there wouldn't be any such thing as damaged radios!" Pretty silly, huh? But people say this kind of thing in defense of physicalism all the time.
(N.B. This is not to defend the existence of souls. It's just to point out that this particular argument against them is invalid.)