You have two problems:
1. Any concentration of benzoyl peroxide in your spot remover is going to be very low; most likely, the sodium bicarbonate isn't the main component of your toothpaste either.
2. Benzoyl peroxide is not a carboxylic acid. You're probably thinking of benzylic or benzoic acid. Those should react, although, depending on the concentrations and mobility within your toothpase, who knows. Benzoyl peroxide doesn't have very acidic protons.