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.
Badges are a great way to show off community activity, whether you’re a newbie or a Champion.Learn more
A blank Trello board can be both a beautiful and intimidating thing. How many lists should I have? Is creating 10 labels overkill? How can I best track my progress? Is there a way...
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
You're one step closer to meeting fellow Atlassian users at your local meet up. Learn more about AUGs