After the Mail Service is/has stopped there can be a large number of emails waiting to be sent.
If you do not want these to be sent out you can run a script towards the database to set all unsent email to sent.
When you after running this script start the Mail Service again there will be no emails waiting to be sent anymore so no emails will be sent.
UPDATE tps_user_message_recipient SET tps_is_email_sent = '1'
UPDATE tps_user_message_recipient SET tps_is_email_sent = '1';