How to Test Auto-Ionization of Ammonia
No, that's not how it all works on more than one level.
First, the amount of $\ce{NH4+}$ out there is small. And by &quot;small&quot;, I mean really, really small - about as small as you can imagine, only smaller. Many times smaller, I must reiterate. If some substance was to react with it (which is certainly not outside the realm of possible) and form a product in equally small amount, you won't be able to see it.
I intentionally avoid any numeric estimates here. You must have seen them already. They are too far outside the everyday experience to make an impression. Well, you may look up the auto-ionization constant of ammonia and see how it relates to that of water (which itself is not big). Guess what? It is many orders of magnitude smaller.
Now comes the second point, which kind of negates the first one. If something reacts with that $\ce{NH4+}$ (which, I repeat, is totally possible), then the auto-ionization reaction will produce more $\ce{NH4+}$ to replace the loss, and then more and more, probably until no more $\ce{NH3}$ is left. How so? Well, imagine a crowded theater emptying through one door. Obviously all those people can't fit in the door at once. Not even half of them can. But they don't have to. They just walk through it one by one, and before long, the theater is empty. Much like that, all $\ce{NH3}$ molecules will go through the form of $\ce{NH4+}$ (or $\ce{NH2-}$) to whatever products are there.
In a way, this will prove that the auto-ionization was there in the first place, but tell us nothing about its extent. To measure that, we need other methods; conductometry comes to mind.
As for pH indicators for water, they are definitely no good for liquid ammonia. They all will be far off-scale, much like your cooking thermometer in the middle of Antarctica. To work in liquid ammonia, one needs to develop a whole new set of indicators. Some seems to be known already, but I have no firsthand experience with them, and Google is the same over there as it is over here.
So it goes.