I've read lots of conflicting scenarios for the Nemo stampede. Seems they change how it goes, depending on the hours, projected crowd levels, EE or not, etc. I've heard: no rope drop; rope drop on Main Street; walking the rope line back partway; walking the rope line back all the way to the queue.
We did it on an EE at 7 a.m. during record-breaking crowds on Spring break. Turnstiles opened at 6:50. Rope drop was at the top of Main. They wound up the rope quietly, cautioning us not to go yet, then said "Go!" at the stroke of 7 a.m. Everybody RAN. CMs calling out ineffectually "Please don't run!" but nobody listened. Through FL, round the back of the Matterhorn, winding through the rope maze. They were ready for us and we were on the first sub in a matter of 5 minutes.
Ick. Too much fuss. I enjoyed our other MM morning much more, heading at an easy walk straight to PP, then walking right onto everything else in FL. Fun and relaxed!
Everything I've read suggests that you should not depend on the monorail first thing. It doesn't usually start right at opening, and it usually will NOT give you a jump on the Nemo crowds.
Some people swear by doing Nemo during Fireworks, F!, or just before park closing.