Dear Graham,
Do you just right-click on the logo picture>Link>Email Address to link the email address to the logo picture and then export the slides to PDF?
If yes, I did a test and it seems that I can't reproduce the issue with PowerPoint for Mac.
About "but when I export the powerpoint into a pdf it does not work nor does it appear as a hyperlink.", some screenshots are appreciated.
Note: Remove any private information before uploading the screenshots.
Regarding "The other links throughout the deck work when they are in written form even when exported.", do you mean that only the specific three logos don't work in PDF?
Meanwhile, I'd like you to provide the file for us to do a test in our PowerPoint for Mac application.
If the file and the file link can be shared here directly, please add your confirmation and add the file link here.
If no, welcome to let us know and we'll take the next step to collect the file.
Moreover, I'd like you to confirm the version number of the PowerPoint for Mac application and the Mac operating system you are using for our reference.
Thank you for your effort and time.
Sincerely
Cliff | Microsoft Community Moderator