Is there a way to play through a story-driven campaign in Starcraft 2 in a multiplayer environment? If its not built-in, are there community-created multiplayer maps that have this sort of feature?
The story driven single player campaign can only be played by one person and cannot be played by more than one player.
However, there is one mission that has been altered that allows 2 players to try this mission on different difficulty settings. http://us.battle.net/sc2/en/game/maps-and-mods/mods/left-2-die
As far as community created multiplayer maps, there are numerous survival types of maps out on the custom games list that players play versus an AI, some are story driven, some are survival. Select join a custom game, then in the category drop down select "Co-op vs. AI"