I would not be surprised to see signage in the parks stating what is and is not available. Most likely the signage will state nothing is available.
We were in Epcot NYE and there was a LONG, continuous line of guests waitingto ask Guest Services about dinner seating --- despite a sign stating there was none, and CMs going down the line and explaining there was none.
I don't expect the near future to be that bad. But seating will be hard to come by. Depending on your party size, you may be eating at third and fourth choices places, or odd times. (Mid afternoon, late evening)