No. The comic element is superior to the heroic element in Much Ado. While there is some ethical action (defending Hero's reputation), and some desire to thwart the wicked (namely Don John), what dominates the play is the lively interplay between Beatrice and Benedick. If you get a chance to see a good production, I predict you'll be much more caught up in the silly tricks everyone uses to try to get those two together, and in the wit of their exchanges. (There are some good movie versions out; you might try the Kenneth Branagh version: http://www.imdb.com/title/tt0107616/ .)
Comedy rules, and the couples happily unite in the end, while the chase after John is put off until another day.