Can an Unseen Servant “wear” clothes, such as a robe or cloak?

Is it possible to put a robe or cloak over an Unseen Servant, potentially fooling others into thinking that the Unseen Servant is actually a person?

The spells say the servant is a "invisible, mindless, shapeless, medium force", but it is unclear to me how such "force" interact with clothing.

The servant can clean, mend, and fold clothes, so clearly it can manipulate clothes in some capacities. The servant can also perform simple tasks that a human servant could do, and presumably wearing clothes is such a task.

However, the Unseen Servant is shapeless, so I’m not sure if it would be possible to put a piece of clothing over it.