The answer is "no", but probably not for the reasons you imagined it.
The most widespread mental model on taste is what I would all "analytical": salt ions hit the receptors on your tongue, your brain notices the signal and you say to yourself, "this tastes salty", and this is taste.
I have the impression that the above model is the one most widespread in contemporary Western culture, but it does not actually explain well the realities of taste perception. This is why modern books on the physiology and psychology of taste usually apply a model more congruent with gestalt psychology: when you taste the food, your brain scrambles all signals coming from all sources at once, and the resulting internal experience is the taste. It is unique to the food you are eating, and trying to divide it up is meaningless.
I understand your question, with the update, to state that eating food with sodium and thinking "salty" is based on an implicit "normal" amount of sodium, and asking if adding more sodium will also cause our flavor experience to be changed without us being able to say that it is due to salt.
If you use the first model (which I don't recommend, since it describes reality poorly), it is possible to speak of "flavor enhancers" in the sense of this question. Remember, under this model, aspects of the taste experience which are consciously matched 1:1 to a chemical interaction on the tongue are the norm, and anything else shouldn't exist, or is at least a phenomenon requiring special explanation. This would match your description of "hidden" taste, which sounds a lot like the concept of salt "enhancing" taste, without your consciousness saying "this tastes so-and-so because of salt".
Under this first model, the opposite of your premise occurs. If you don't notice the effects of salt on a food, this is usually the food contains less salt than the amount that becomes salient. You might not recognize the salt in a slice of bread, but you will sure notice that brined herring is salty. This means that the flavor enhancing effect only happens when the food contains small amounts of salt, not large ones. Thus it is not "extra" salt on top of the salt you notice is there. If they were to add extra salt to salty food, you will still notice the salt, and it won't be hidden.
Under the second model, the question becomes meaningless. Since in this model, anything in your food is a contributor to the unique whole experience of taste, being an "enhancer" is the norm for all things in the food. A food containing so much salt that you also makes you recognize its contribution and say "oh, this is salty" is something that happens occasionally, and is possibly more an artefact of how we have learned to think of food (a normal person has learned to associate a taste with a particular profile with salt, while a wine taster has also learned to associate a different flavor profile with berries and notice when it is present or absent in wine). The contribution of recognized and unrecognized aspects to the whole of taste is not qualitatively different, and the attributions we make are not necessarily a true description of what is going on chemically on the tongue. So, declaring part of the taste a consequence of "normal" salt and another part the consequence of "extra" makes no sense. Since the concept of "extra" salt is meaningless, it obviously cannot be found in food, be it from industrial sources or otherwise.