I have our FDP at Mama Melrose's scheduled for 6:20 pm.
Last year, our FDP was scheduled for Hollywood & Vine for 6:30 pm, and I think (if I remember correctly), I was checking us in around 6:00 pm.
I can't remember how long the parade is, but I don't think it's longer than 30 minutes.
When you're deciding where you're going to sit for the parade, look at a MGM map to see where your restaurant is (especially if you feel like you're "cutting it close") & position yourself where you can get to the restaurant w/o having to go against the "after parade" flow of traffic.
Edited to add - If you wanted to eat BEFORE the parade, I would try to get an earlier ADR - maybe 4:00 pm? Depending on the time of year you're going, that may not even be enough time - considering that to get a good seat for the parade, you need to be there around 30 minutes prior to the parade start time (if not before).