No DHCP doesn't mean public IPs nor impact the need for NAT, it just means the hosts have to be explicitly configured with IP addresses, default gateways if they need egress, and DNS.

Those IPs you end up assigning manually could be private ones or routable ones. If private, authorized traffic could be bridged onto the network by anything, such as a random computer with 2 NICs, one of which is connected eventually to the Internet and one of which is on the local network.

If public, a firewall can control access just as well as using NAT can.