Can users disable email notifications sent to them by Rules?
Unchecking the box for the contact form only affects the personal contact form provided by the Contact module (part of Core).

I added a similar feature (allow users to opt out to e-mails sent via rules) to a Drupal 7 site in the following manner.

First, I added a field (Boolean single on/off checkbox) labeled "Send me notifications" to the user account page.

Then, I made a couple rules to award a role nomsg upon checking the box and to remove the role upon unchecking the box.

After that, I created a rules component of type condition that checked to ensure that the user did NOT have the nomsg role.  I then added that component to all rules that sent e-mails.  This was a bit of a pain, because some of the rules that sent e-mails also did other things, so I had to break out the part about sending the e-mail (as another component) so that the other actions would be performed but the e-mail would not be sent if the user had the nomsg role.