Sorry, but I cannot really add any more to what I've already said. I went through this again to double check as follows:
I opened my Mail application, which displays a mail account that is using an AOL email address
(If you are using a different type of email address, then things may not be the same as AOL)
I clicked on the In Box to display current email messages in that mailbox
Opened up Time Machine and gave the application about 10 minutes to load
The current messages in the In Box are displayed
I clicked on the timeline at the right of Time Machine window and selected a date about a week ago
Time Machine took a few seconds to display the In Box for that date, which was of course different than the current In Box
There is a Restore button at the bottom of the In Box display. If I click on Restore, the week old In Box will appear in my current Mail program and I can look at the messages that way.
But, to do this looking for hundreds of different emails on different dates is going to take tons of time. I can't guess how much time would be involved for something like this.