Email sent to blank address on email change for user with no previous email address

[knutsp]

1. Install/active some email logger og logging functionality for outgoing emails
2. Import some content from other WP site
3. Let importer create a new username for some of that content, when prompted
4. Edit the newly created user and add an email address
5. Observe the email log: "To:" field is empty

Expected: No email (attempted to be) sent when previous email is blank.

[johnbillion]

Out of interest, does WordPress also try to send an email to this blank email address when someone leaves a comment on a post belonging to the user? Or when the user requests a password reset?