I suspect the answer is no and that I will be directed to CSV Rendering Design Considerations & CSV Device Information Settings.
However, it seems not a little unintuitive for this to be a global rather than per report (or even per table) setting.
I am not (currently) set anything about reports programatically, my set up is simple, I have a report template on the report server that I run via the REST API and download the output document as a CSV.
I could, after downloading, then open the file and remove the header row. But I'm hoping that I am incorrect and there is some obscure report template setting somewhere, or perhaps an argument I can pass via the the REST api, that might allow me to decide on a per report basis how table headers are treated in CSV format.