I am developing a headless implementation of Magento. Do I still need to use Fastly as a CDN service for it?
No, you don't. In this situation, you may skip using Fastly — at least, in the beginning of development.
"The only situation you may not want to enable is for a headless deployment."
Still, most probably, you will need Fastly for using its SSL certificate.
All Magento Commerce (Cloud) Customers get a shared SSL certificate from Fastly as a part of the Cloud subscription plan. Adding own SSL certificate to Fastly is a separate and rather expensive paid option. Thus, we strongly recommend to enable Fastly and, at least, test it on Staging and Production environments before going live — even for your headless Magento website.