Yes, each savings code is used just like a gift card towards payment, rather than a coupon. So you could use all 3 savings codes and your gift card (s) in the same transaction if you'd like. Keep in mind though that the savings codes aren't available immediately (unless they glitch) and if you need to return something the terms state "The value of the savings code will not be refunded if merchandise is returned or an order is cancelled." I have no experience with that as I only used them on GCs when we could do that before so I wasn't returning anything anyway.
You can also order one $450 GC and still get 3 of the $15 savings codes emailed later. (or a $300 and get 2 savings codes)