It's not a feature already built-in implemented, but if you want, you can build a report against the internal Tableau Postgres repository that looks at table historical_events for the event_type_id equivalent to publish, and then you can subscribe to this report.

Like Jeff said, it's not a feature. But you can easily build this as a conditional subscription from a viz that uses the TS Events data source I wrote. You'd download it, open in Desktop, point it to your Tableau Server repository database, then put Item Name on Rows, filter Event Date relative to the Previous day, filter Event Name to "Publish Workbook", and filter "Actor User Name" to just your admins. Publish to Server, and subscribe to the viz on a daily schedule with "Do not send if empty" checked. Data driven alerts would work for this too, but it's a few more steps to set up.

Yep, I tried the built-in TS Events, and it seems to work great for this kind of stuff.  Gilbert, here's a screenprint of what it could look like (the event date is set to relative TODAY).

It's inclusive of the publish event.  Look at all the available values for "Event Name".  The one I show in the screenprint is inclusive of new workbooks being published and updated workbooks being published.

For a workbook publish action, there will be a single "Publish Workbook" event, which will will correspond time-wise with several "Publish View" events--one for each view published.