No, understanding tables does not imply a deep understanding of dive physiology just like mastering addition does not mean you will join AP calculus. Nonetheless I still firmly believe that a diver trained on tables and square profiles will have a better understanding of nitrogen accumulation and decompression. More importantly it imparts the fact that the dive computer and it's alogarithms are not absolute and that at all times common sense should trump. Something that someone conversant with tables will best appreciate.
How on earth does learning tables teach you that the dive computer is not absolute and common sense should trump? That one has me totally mystified. How do you know that someone who has learned the tables must have a better understanding of nitrogen accumulation than someone who learns on a computer? As I said, my whole training on this comes before I teach either tables or computers, and I teach it the same way for either class.
Perhaps the most celebrated book explaining decompression theory today is Mark Powell's Deco for Divers. He does a great job explaining decompression theory in great detail without once teaching how to use tables to measure it.
By the way, you comparison using arithmetic and calculators is a false analogy. In order to get by in today's world, unless you are in a pretty much no math situation in your life, both the ability to compute by hand and the by calculator are necessary life skills. Schools still teach both, and for good reason. To a certain extent, you must have the basic manual competition understanding to use a calculator. But that only does so far. In math classes, you probably learned how to calculate square roots by hand. Do you think the ability to do that by hand is a critical skill, or is it OK to use the calculator to find that for you?
In contrast, there is no need to understand the tables in order to use and understand the computer. More than 100 years ago, John Haldane tested goats in order to find a way to make people safe from DCS on ascent after being under pressure. He had to figure out a way to make the results of his research usable to the population that needed it, and he created tables for that purpose. If he had done his research in a more technically-advanced era, he might have created the first computer algorithm for that purpose instead. If he had done that, there is a good chance no one would have invented tables. If that had happened, none of us would even know what tables were, and no one would be arguing that you need to know the tables in order to understand what the computer is doing.