Hi,
You don't need to add a 0 price. What you need is to restrict the existing price so that it is not available for the user groups of that user.
That way, the system won't see the price and will let the customer go through the checkout without payment.
Now I suppose you could also create a price of 0.0001. This would save and it would still be 0 on the frontend, but you'll still have to configure the access levels of both prices so that your special user only sees the 0.00001 price and the other users only see the normal price.
A simpler alternative to all of this would be to not touch to the prices and just configure a 100% discount for that user in the Orders>Discount menu. That way, it will apply to all the products at once, so it's a lot simpler to setup.
Note also that if you don't mind not having orders, you could use the barcode stock manager plugin available on our marketplace.
It allows the user to easily find products in the backend and add / remove stock on the fly without having to go through the whole checkout sequence.