You should be able to do that look for the most part yes. It may be just a little different, but should work out.
The biggest issue here for you though is that there is no email payment situation or email ordering setup in the program. The only way you could do what they want done is to incorporate a form for people to order from and put that on an Order Here page or something. People would have to browse the shop as a Catalog (which you can setup that way so that ordering cannot be done on the site, just browsing), and they would have to keep track of what they want via product id's or something and then put them into the form to order.
The above has worked for quite a few people that don't really want people to order directly, but unfortunately, it cannot be setup to take outright email orders via the cart itself. The cart does setup a great catalog website though so I would definitely check it out and see what you can do with it.