How is the email form supposed to work in the 'Notify Me' section?
Which email form ? From our plugin or from Joomla component?
Where did you saw "Notify Me section" ?
In VirteMart ? If yes .... Notification will work when your product is out of stock and you must set config in VM admin as: Displays 'Notify Me' instead of 'Add To Cart' button.
OK, now I see. Use module from Newsletter component (for example: Acymailing Starter) if you want to collects peoples e-mails and have lots of features.
p.s. Modules can be placed inside articles, so this is not a problem to replace this simple form with this from module.