The SSB series does not revolve around a storyline, it revolves around multiplayer. Having said that, you aren't going to be 'confused' or anything, because Brawl is actually the first time that a SSB will have a storyline to follow. Playing Melee would definetly help you understand Brawl quicker, though. Many things will change in Brawl, but you will have gotten down the basics.
All in all, you definetly do not have to have played Melee to understand Brawl, but it would help you become better at Brawl quicker.