Yes, but not through core BuddyPress, BP User Todo List adds category-based task organization as one of its main features.
How Categories Work
Members create categories and assign tasks to them, giving each person their own organizational structure rather than one flat task list. Tasks themselves support a name, description, due date, and category assignment.
A shortcode, [bptodo_by_category category="CATEGORY_ID"], displays tasks from a specific category anywhere on the site, a page, a template, wherever it’s needed.
Other Features Worth Knowing
Tasks can be edited, deleted, or marked complete. Due-date reminders go out via email and BuddyPress notifications, with admins able to toggle that on or off site-wide. Tasks export to CSV for backup or use elsewhere. Admins can also disable category creation entirely if a flatter task list fits the community better.
Pricing
Free (v3.5.1, updated within the last year). Download it here.