Do I really need the wire from the alternator to the bulkhead connector?

If you want the factory ammeter to work, then yes, you need it. If not, then you can run a large gauge wire (forgive me I cannot remember the correct size) from the alternator to the large stud on the starter relay. This will effectively render the ammeter useless, as it will not read correctly any longer.

I've thought about doing it to my car, but everything behind the cluster is in good shape and I have no melted connectors anywhere. THe only things I have added electrically are the electronig ignition and a decent stereo system....although it has no external amp, so no big draw there. My ammeter works great and all the wiring is in good condition. So I don't plan on modifying anything at this point.