When we were there 2 weeks ago, the parade was at 5:30pm. We missed it both times we were there because of early dinner ADR. I would say to go for a late lunch or anything after 6:15pm or 6:30pm.
We are going in Aug, and the parade at MGM is a must for us. Grandson HAS to see the Power Rangers! When making my ADRs, I asked about the parade, and was told it would last about 30 min., and I made my Sci Fi ressies for 6:25, which she felt would work out well.