generally with the term coating we actually indicate a technological product that is much more complex and that we could more correctly define as "coating system". This is because what goes to protect the substrate is composed of at least 3 elements: surface chemical treatment of the substrate, primer and top coat. Each of these components plays a pivot role as it can promote adhesion, substrate protection, aesthetics, antifouling properties, etc. Naturally these properties are obtained only if the different components are applied strictly following the indications provided by the manufacturer (eg pot life of different layers, environmental conditions, etc.). But, at this point, why do we often use inhibitors or other protection systems (eg cathodic protection)? In the event of damage (eg mechanical) of the coating system we must preserve the substrate using a protective layer in the system itself (eg galvanisation in the automotive sector) or external supply (eg corrosion inhibitors in closed systems).
as i said before, in case of coating damage or less coating protection power, the corrosion inhibitors can help us to preserve the substrate, if used in suitable conditions that depend from the "real" applications (eg if I have to protect a closed system or open to the environment).
some years ago, I studied a hard case of acidic medium in a desulfurization plant where, in some areas, a solution with a high concentration of sulfuric acid was formed at high temperature. Even in this extreme case if the choice of the coating was made with criteria and all the application specifications had also been carried out, a "thick" layer of suitable organic coating was able to resist. If the operating temperatures are increased beyond the set threshold or the coating is not applied according to the suitable protocols, the damage generated can be very high. In your specific case, I would focus on the aggressive medium and the material to be protected; you will surely find in the literature or through experts in the field the best type of protection (... and any other precautions) necessary for the proper functioning of your product.