I think this use is fine. To revise it with something like "who are not persuaded and therefore remain uncured" seems cumbersome.Here is my paragraph; as you'll see, i actually use "remain unpersuaded", which is the expression mentioned by B.:
"For it could be possible that a therapeutic argument with true premises and a valid form of inference according to the standards of traditional epistemology and logic was regarded as unsound by a given patient, who would thereby remain unpersuaded, and hence uncured. And it might even happen that this patient remained unpersuaded by all the sound arguments on a given topic one could advance."
If you used thereby because you want to say 'by this means', I would suggest something like "who would remain unpersuaded by it".(You might be right about "thereby"; now I'm not sure either.)