Hey Christopher!
I do recommend making an Advance Dining Reservation if there is a restaurant that you are eager to try. Just in case it gets completely booked before you arrive
My family eats very early, also, and have always been amazed at how full the restaurants are at all times in Disney World!
Just seeing the crestfallen looks on Guest's faces when they are turned away from one of the fabulous restaurants in Epcot's World Showcase because it's been booked for months has convinced me to always make a reservation. Being on Disney's Dining Plan wouldn't make a difference concerning getting a table for dinner.
Last year we decided to ask if we could get a table at the Rose & Crown restaurant for an early 5pm dinner. We lucked out and they were able to squeeze us in...but it was after a 30 minute wait! We watched people who had ADRs walk straight in. I admit, I had table envy!
So, it is possible to get a last minute table in a Disney restaurant, but you never know if it's already fully booked. My husband and I know that we always want to eat at the Table Service restaurant in the Germany Pavilion so that is the one ADR that we always make...the rest we leave up to chance or stick to Counter Service.