If the net connection was only used for delivering apps and email from remote servers would the green/blue line be better?
The local server being for printers & files.
No, having both a firewall and software protection on the server is best for security. It doesnt take much for serving up files and printers, often printers have their own direct NIC so the server can ignore that if required.
My network doesnt have one but every PC on the network has Zone Alarm on it.