Yes, each team member can have their own private workspace! Their private workspace will not be the same as the workspace you are sharing with them.
That means that, in addition to the workspace you and your team members are all a part of (which is not private and all projects within are accessible to all team members - editing permissions will vary according to their assigned roles), they can each have their own workspace, which is independent of the shared workspace, and does not profit from the plan subscription.
Since each workspace is private by default, only the team member who created the workspace will be able to access it.
Be aware that when you invite others to collaborate on a workspace, the workspace is no longer private and the people who joined it will have access to all its content.