This question has been answered by BobRay. See the first response.
One way might be to use FormIt2DB to process the form.
The more "official" method would be to have create and update processors and post the form data to them. In the processors, you'd use xPDO to alter the database (right after the email is sent).
In a typical CMP, the menu item launches an index.php file. The index.php file launches a controller that creates the display and handles requests (e.g., mouse clicks in the form).
The request handler routes the request to a connector file which calls the appropriate processor. TBH, I'm not sure of the details on how the return value from the processor is handled. I think it comes back to the controller vie the connector.
In the usual JS setup, the mouse clicks on the form trigger Ajax requests to the request handler, but I don't think there's any reason that a standard HTML form couldn't do the same thing.
Someday, when I have time, I'm going to create a complete CMP with no JS at all, just to figure it all out.