Hello,
No, this option is a Personal Setting by user, so there is no a OOB functionality to change the option for all users or entire organization. The default value for Track option is "Email messages in response to Dynamics 365 email", so if the user didn't change that, the mailbox can be enabled with no additional validation from administrator side. Also, you can use this tool "UserSettingsUtility" from XRM Tool Box, to check Personal Settings for users and change that through bulk way:
www.xrmtoolbox.com/.../
*There are several articles into community about "how to use" this tool.
Thanks,