When I went back in March 2017, we hit DHS during the EMH. We weren't at the front of the pack, but my group was walking up the street at rope drop. They went over to sign up while my son (who was too scared to do this) and I went on Star Tours.
After our ride they still weren't through the line, so we went to TSMM - not sure when they finally got through the line .. I think they spent most of their EMH waiting in line and had a 3 in the afternoon sign up. I can only imagine during a regular park opening that it would be just as bad. Seems like the available slots would fill up pretty quickly.
So I would say, yes, you need to get there at RD.
While I would love my son to do that, I am sorta glad he was too scared to try it -- that would have wasted our EMH (on a day we were only planning on spending half the day there anyway).
Frankly, it seems so popular that I am surprised they haven't changed this to a hard ticket event type of thing (would keep demand down and maybe let the kids keep their lightsaber or something). It would probably be just as popular.
Maybe they will with the opening of SWGE ..