From the looks of the wiring diagram, there's no neutral switch on the HST version of the
L3400. Which means you can start it in any range as long as the clutch is depressed. As soon as you depress the HST pedal, it brings the seat switch into the loop, which looks for weight in the seat. Under those conditions, the only position of the seat that won't kill the engine is fully down with an operator in it.
The DT (gear) version of the tractor doesn't have a clutch switch, however the shuttle or range select lever must be in neutral before the starter will engage. In both versions, the PTO must be disengaged to start the engine.
At first I wondered about the lack of a clutch switch on the gear drive version that I have, then I realized it allows you to start the engine while you're standing on the ground as long as it's in neutral. Handy for warmup or running the hydraulics, but I still always check to be sure it's really in neutral before turning the key. You're standing right in front of a rear tire when you turn the key, so if the neutral switch isn't working you're in a world of hurt if it goes ahead. It's easy to develop bad habits, something you have to remember when you run somebody else's tractor.
To answer your question Katahdin, yes it should allow you to use the hand throttle, even if the transmission isn't in neutral since there is no neutral switch as far as I can see. You just can't touch the HST pedal. James (K0ua) had one of these a few years ago, he should be able to say for sure. I'm not sure if northeastern was using the hand throttle or pressing down on the HST pedal with the trans in neutral. If it was still dying using the hand throttle I'm at a loss as to what is going on, unless it's running out of fuel instantly for some reason. Being in neutral shouldn't make a difference if you press the HST pedal.
Sean