This was a couple of years ago now so things might have changed. But DH and I were running late for our MM. By the time we got there, there were already massive lines for all the rides. Feeling a little lost and disappointed, we wandered back to Town Square.
At Town Square there were a few characters with practically no lines! I got a photo with Pluto, and I believe Mickey was also out, but they went backstage before I had a chance to see any more.
We then sat on one of the benches to figure out the next plan, when some more characters came out! There was literally no line for the Queen of Hearts, Donald or Goofy, and we had great interactions with them. Donald and Goofy then went backstage, and the Queen of Hearts joined the marching band, Alice and the Mad Hatter (not sure where they came from) and headed to the turnstiles. I assume they were going to do some official opening thing.
It's probably not worth missing out on the rides for (unless you're more into characters than rides I suppose, or miss the boat with ride lines like us), but assuming they still do it, there was definitely a chance to meet characters during MM.