There will definitely be reservations still available, but not for the high-demand restaurants. We just decided to go on April 8th a couple months ago and we were able to get Raglan Road, 'Ohana (9pm was the only available time), Biergarten, and Olivia's. We weren't able to get Be Our Guest, Chef Mickey's, or Cinderella's Royal Table.
Anyway, I know how you feel. We've been planning to meet my cousin, her husband, and their 3 kids while we're there. They wanted to get together for dinner, but I had to bug the crap out of them for over a month to get them to tell me what day they wanted to go! They're going with the dining plan and haven't made any ADRs!
They've been before, but never with DDP. I've told them over and over that they should really make ADRs if they want to get into their first choice restaurants! I'm sure they'll flip out when they see the BOG line for lunch!