Q: Does Exchange Server 2016 require an Edge Transport server to be deployed?
Edge Transport is an optional role, which has been the case for all versions of Exchange that have had an Edge role available. The consolidation of Exchange 2016 server roles into just two (Mailbox, and Edge Transport) doesn’t change that. You can deploy a simple Exchange 2016 environment on a single Mailbox server, with no Edge Transport server deployed at all.
What you might need to consider though, is whether Edge Transport does anything for you that you need from a functionality perspective. The Edge Transport server role is designed to sit in a perimeter network, providing secure mail flow in and out of your organization. That includes filtering unwanted email, although the capabilities are not as rich as most other email security products and cloud services (including Exchange Online Protection). So from a functionality perspective, you may still need to deploy an email security server or service to protect your environment and your end users.
You can read more about the Edge Transport server role here (the article is written for Exchange 2013, but little has changed for 2016).