It's s a much needed feature, YES. I had an idea to solve it. But it has a drawback. The idea is to create a product that is the amount owed after deposit, only. In the description text, state the deposit amount, but it's just in the description. So it says : Total, X less deposit X, amount due X. " Create a password protected page and put that product in it. Send an email with a link, the password, and a request to complete payment. After the payment, you can make the product hidden until you need it. You can change the password, change the amount, or you can create a series of "completion" products of different value amounts that you turn on and off as needed. The drawback is that the "product" cannot be totally hidden from public view. But who will likely find it or buy it anyway? Imperfect, but doable, at least.
Feature request number two: Hidden from general public products that can be bought. Even if the "shop" is not linked , Can't do it without the potential someone will find and try to buy what they think is a product for general sale.