Hi,
It's possible yes.
First, to make sure that no one else can see the product, you can create a specific user group via the joomla user manager, add the user to the user group, and use the "access level" option of the product to restrict it to that user group. That way, only that user will see it.
Then, you can give him the link that you get when you click on the "Add to cart HTML link" button of the product edition page so that when he clicks on it, the product is automatically added to the cart and he gets redirected to the checkout.