This is an available feature with business class.
In Business Class, you have the ability to see what boards a team member is a member of, and their assigned cards. Here's some detail and sample of that http://help.trello.com/article/714-business-class-user-guide#View-team-members-activity-boards-and-cards
Keep in mind that in order for this to work with Business Class, the user would need to be a member of the actual team, and not just a member of the team board.
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