Yes, you can have multiple Connectors running side by side. If you are running Connectors, I assume that you are using PAC file to redirect the web traffic to the Connector, right?
You would need to add the new Connector ip address/hostname to the PAC file.
For continuation of service, yes, the PAC file will be configured with those Connectors and browser will check the proxy ip address in order. If the first one in order is not responding, it will go down the list until it finds a responsive proxy.
Agent.properties is only the configuration file. You would need to install the Connector software first (using the Connector.exe file), then copy across the agent.properties file.
If in doubt, feel free to open a TAC case and an engineer can assist you with that.
Hope that helps.