My organization does not have an internal DNS server. Is an internal DNS server required to sign up for MDBR, or can we manually point each workstation towards the Akamai DNS servers directly?

An internal DNS server is not required. You may configure the DNS settings on each individual machine (DHCP would be the easiest way) or change the DNS settings on your router. If your environment is very small, you may be doing DHCP on your router and could alter both settings on that device. CIS would need to know your organization’s public IP or public CIDR netblock.