The only difficulty is setting up a product that;
(a) only the relevant customer can see
(b) the product does not show in any of the product lists or menus
If you can easily solve (b) without too much code changes...(a) is fairly straightforward.
You could write some sort of admin page which allows you to;
select a customer
fill up that customers cart
Then ask the customer to login where their cart is waiting for them.