Outlook provides Rest API calls for getting your emails. Using this you can grab your mails as JSON response.
https://msdn.microsoft.com/en-us/office/office365/api/mail-rest-operations
you can filter the results using their select or filter comments.
TestComplete provides an option to do the request response.
https://support.smartbear.com/testcomplete/docs/reference/program-objects/aqhttprequest/index.html
This gives you some hope that you can actually verify the or get value of the mail without outlook installed.
If you start your analysis from this point, you will be able to found a answer for you
