That question is almost impossible to answer for a number of reasons, including the ambiguity of the definition of edibility. For example fuchsia, commonly grown for flowers, actually produces edible fruit, but it's flavorless, barely sweet, and usually bitter. There are many plants that produce edible fruit that nobody would eat unless starving.
I think it could be done, but it would be a Herculean task, and nobody, no company, or institutions, is up to it. If a comprehensive inventory would be created the fruits could be broken down into categories to avoid the problem you are talking about. For example: 1) fruits that are marketed or have commercial value, 2) fruits that are not commercial but well appreciated locally, 3) fruits that are edible but not usually eaten, 4) fruits only eaten during famines.
Documenting it would have value beyond just counting numbers. For example you could get clearer idea of what plants of value are endangered or in risk of becoming endangered. Obviously mostly ones in categories 2, 3, and 4.
If each country published its own fruit inventory then it would be a lot more doable, and a whole lot more complete, as a world compendium would just mean bringing all country's inventories together.
I think in the case of Brazil you have Lorenzi who is doing something similar with Brazilian fruits. If each country had a Lorenzi then your wish might come true!