You can turn on the email-Logging on the administration page System > Troubleshooting and Support > Logging & Profiling. Then you can parse the generated log-file atlassian-jira-outgoing-mail.log to calculate the number of emails (independent of the recipient of the mails).
Corporates use different setups for email so not with every email program you can check the sent mails. In some organizations it may be possible, but in some organizations it may not.
My suggestion is you should talk to the person who's administering the mail servers in your organization, and check if the statistics are available.
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