Directly in-app, as a feature, no this isn’t possible. However if you have a pipeline engineering resource, you could achieve this using our ecosystem of APIs.
For the case of creating a Note when a Task is changed status, you could use an Action Menu Item. This would appear as a right-click option on the Task which, when clicked would delegate information to a web page that you’ve coded. This web page could take input of the text for the note, create the note and change the Task’s status.
For information on Action Menu Items, please check out these resources:
As for the reverse case where creating a Note would trigger a change to the status of the Task the note is linked to, you could use the Shotgun Event Daemon or our forthcoming Webhooks (currently in closed beta). With either of these two approaches, when a Note is created a signal would be sent to your code via either framework. Your code would look at the Note, find the associated Task, if there is one, and change the Task’s status to the appropriate state if the Note matches the requirements.
For more information on the Shotgun Event Daemon please check out these resources: