It should work...
Thats not how the factory wired it--but when adapting a GM altentor to a tractor or other equipment,thats how we wired them up,and they always charged..
Check for power at the brown wire with engine running,with a test light--it should have 12v there-(and so should the red wire!)-if its dead,it wont charge--it needs 12v to "excite" the feild coils in the altenator to make it charge--it takes power to make power..
If the brown wire has no juice,its probably broken or corroded somwhere in the harness,or where it goes into the fuse box--you can run a wire from the battery positive terminal to the brown wire right at the altenator plug,you will hear it "kick in" and charge if the brown wire being dead is the problem...a quick test to see if its charging is to hold a screwdriver near the rear bearing cap in the center of the altenator--a strong magnetic "pull" indicates its charging...
If both wires have power,then its likely the altenator or regulator,diode trio,or rectifier bridge inside it is junk--time for another altenator,or rebiuld it....

--Hope this helps....
