We're about to start selling gift vouchers, but the email template we use is more geared to shipped products. Can I do some kind of if-else to specify what the email says, depending on whether the order has a shipped product or not?
Yes, you can, but you're going to need a developer. That's quite a complex modification to the email templates. It's probably worth posting the job for a Neto Partner to look at. Some of them have a lot of experience with email templates and could tailor it just how you need.
https://www.netohq.com/job-request-portal