No, adding a document specifically to the task will not add the document to the property. This means the document that is added to a task must also be added to the property in order for it to be visible under the property page.
Due to the high amount of tasks a property will likely acquire, the corresponding task documents remain attached only to the task page to not clutter the property page. If a task specific document is particularly important for the property notes, be sure to add it to the property documents as well.
You can only add documents to a task after the task has been created.