Not quite, but you can come close. In your menu go to Project, Group. In
the Grouping dialog box choose More Groups, New (group). Create a group
which uses the Resource Name as the first level outline field and apply it.
You'll see the tasks arranged by each resource assignment. Use the outline
tools on the formating toolbar to collapse the task and you'll see just the
resources. This isn't quite the same thing as what you describe because if
you have 2 resources, Joe and Bill, and you assign them to tasks so that
sometimes just one of them is on the task and other times they're working
together, you won't just see two task groups but rather you'll see three -
"Joe", "Bill", and "Joe, Bill"
Another option is the Resource Usage view. It will show the hours of work
against the timescale instead of pretty picture bars but it does reveal the
same information, and more, that your Gantt-type view would show - how the
resource's workloads are distributed over time.
Hope this helps ...