You can do this but it requires a bit of coding work because you need to:
Create the form that shows on the product page asking for the user's email
Save these email addresses in a database table ready for when the products are back in stock
Write a scheduled process that regularly checks stock levels and emails customers when stock is available, then removes their email address so that they don't get repeated emails
What would also be good is to report on those out of stock products that are receiving the most stock enquiries
I probably can't promote third party products on here, but there is a module that does this for you. Simply search in Google for 'email stock aspdotnetstorefront'