Hi Jwern,
The rules for the customer sign up form may be different than the newsletter form, which is why you’re not seeing mention of the note attribute on the docs for the newsletter. I’m thinking since the newsletter doesn’t truly create a customer, only creates an entry with the email address without other details, the note wouldn’t be supported.
It looks like the note can’t be added on a customer registration form if the customer already exists - ie: this form only creates a new customer, but it doesn’t update an existing customer.
Could you use a newsletter sign up form instead and add a custom field that would save the note as a tag on the customer (see this post with a description of this)?
Otherwise you could check what apps are available for updating existing customer accounts.