I think we may be talking about 2 different things here. I call the neutral lock the thing that prevents you starting in gear. The lever you are referring to is what I call the "fast idle" control. And yes, it will work.
As for that control box, again if it's a honda "plug'n'play" then in theory it should, as the big electrical multicore will have some warning functions built in. The second wire, if you look closely, terminates in another plug afer about 6" of wiring. (but the photographer has decided to make the pic look tidy - it's hidden under the big coil) That is for your tacho. You may also find that although the electric start does nothing in the way of cranking your engine, you may need to have the key in and "on" for it to run - the "off" position of the key switch is usually wired to the same circuit as the deadman. On the plus side, it's another security thing against opportunists jumoping in & driving off.
The text says it's comapatible with a BF15D. If that's your engne it should work. As I said before, check with the dealer before you buy as I've never used one of these engines on remotes.