Adding new alternator

YUP. This will allow the existing throughputs in the bulkhead connector to share the load. If you don't have some high current stuff -- like a big audio system -- taking power from the interior of the car, you will be good.

Only other issue now, would be the other connections through the bulkhead, ignition, lights, etc. Check your diagram, probe the bulkhead connector with the car running to compare ignition and lights voltage to battery voltage, to make sure there's no/ little drop through the connector.