If all of the restaurants in MK, or any other park for that matter, are booked (yes, every single one!) does that indicate the park is going to be packed that day?
No, it doesn't. There are only 5 TS restaurants in MK and there is room for a lot more people in the park than in the restaurants.
Even in the other parks, the capacity of the parks is much greater than the capacity of the restaurants (Animal Kingdom, the largest park, has the fewest restaurants). Free dining pretty much ensures the restaurants will be booked. It does not ensure that those who booked will actually show up for their reservations though.