Yes! Offering gift notes to your customers is a great idea. If so, adding a gift message option is a must.
It's very easy first you must add the note on the Shopify store and then your message will be imported on the gift note section on the order. The gift invoice will hide the cost and billing address.
Please reach out to firstname.lastname@example.org or let your onboarding specialist know if you want gift invoices applied to all orders.