Yes, the cart will work with just Add to Cart buttons and only one script line as mentioned above.
However, we strongly recommend having a View Cart button if there's any way you can manage it. Not having a View Cart will adversely affect your conversion rate.
If a buyer clicks Add to Cart and wants to continue shopping on your site, without a View Cart button they will have no way to bring up the cart again, and they may not want to click another Add to Cart button to bring up the cart if they don't want to order another item, so in that case they may just abandon their order entirely and leave. View Cart gives them a way to continue shopping around your site and then bring the cart back up when they're ready for checkout without having to "risk" adding more items to their order than they wanted to buy.