I'm trying to send hundreds of customers a gift card as part of a promotion we're running and I don't want to do it manually one-by-one in Shopify's backend...
It's definitely possible! If you're on Shopify Plus your rep can definitely help you do it, for the rest of us there are some Shopify apps that allow you to bulk import a CSV of the customers you want to issue gift cards for and automatically create the gift card codes. Most of these apps also allow you to email them out with a nice template.
This app includes that feature and a whole suite of other gift-card related features as well:
