I don't have a dot in my email but I signed up an Amazon/Audible account with a dot in it. Now I am trying to get a refund but they need the email to be sent from the email address with a dot. I went to settings and added the email with a dot in it with "alias" checked but when I send a message to a dummy account, the dot still doesn't appear.
Dots don't matter in Gmail addresses
If someone accidentally adds dots to your address when emailing you, you'll still get that email. For example, if your email is firstname.lastname@example.org, you own all dotted versions of your address:
Note: If you use Gmail through work, school, or other organization (like yourdomain.com or yourschool.edu), dots do change your address. To change the dots in your username, contact your admin.
I guess that would be the same reason why you can't set up a doted address to be shown in the received email.