no the alternator is a required part, you unhook the alt the truck will not start. current passes through it, weather or not its good and pumping out 14.5+ v.... you can not unhook or by pass the alt without other wiring mods. check the larger side wire that goes to the stud on the alt. that was my issue, bad connection. its a power wire, not a ground so it can stop current at that point if its bad.
check your connections with the new conversion... check the cables as well and with an alt being under water unless it was clean water, they dont like that and you could cook the internals of one. have you have a brake light on in the dash and or a charge light? the two of those together indicates a bad alt. also you might want to check fuses under the hood -i doubt thats the issue as you are still getting a click click, but yeah. my bet is still on the wires, possibly one has some hidden corrosion that you can not see. have you tested the resistance in the wires/cables?