Does the DNS service need to be on in order for the caching service to work on OS X Server? I didn't think that caching needed the DNS service to be running in order for it to work. Is this true/false? I've been reading a lot of forums where it says you should get the server DNS right in order to make sure all the other services work but I just wanted to make sure.
It depends:

If you plan to provide the Caching Service to clients with public IP addresses (in other words, not behind a NAT) that are not on the server’s same subnet, you need to create a TXT DNS record in your zone file for the server with the IP address ranges the server is responsible for. Source

If you plan to provide Caching Service in all or any combinations or portions of subnets of the local network that share a common public IP address you don't need a DNS-Server.

Please check the limitations of the Caching Service here.