An amount of soda sufficient to make you ill would be very VERY detectable in food. Speaking as someone who makes their own honeycomb toffee and soda bread, it's really easy to mess up the ratios and end up with an excess that tastes nasty, and that excess is pretty small.

A small amount won't make a different, it'll just stimulate a bit more H+ production from your stomach's proton pumps.

Edit: The article I read claims the scam involved baking powder, which makes even less sense given that it's even more noticeable, bitter and metallic.