Can aniline autodeprotonate? I had an argument with an assistant in my lab, as he stated that in a hypothetical reaction two aniline molecules could react in a way, that one takes a proton off of the other one, thus creating a $\ce{R-NH3^+}$ and a $\ce{R-NH^- }$

However, the $\mathrm pK_\mathrm a$ of aniline is 27, which means, that it is, if at all, a very very poor acid, making it in my eyes impossible to deprotonate. Maybe it could be possible with n-BuLi, but that was not part of the reaction. The main topic was a nucleophilic aromatic substitution to 1-bromo-4-nitrobenzene, with aniline. 

Is it even hypothetically possible for such a deprotonation in pure aniline to occur?
I'm going to side with you @TheChemist. 

Your TA might be suggesting this because you need often need a negatively charged nucleophile in order to carry out nucleophilic aromatic substitutions.  

Having the nitro group in the 4 position makes the your electrophile much more receptive to attack, since the negatively charged intermediate will be resonance stabilized.  

Even if the one aniline does deprotonate another, the concentration of the deprotonated anilide will be so low (on the order of 5 x 10-28 mol/L in pure aniline, if the pKa is 27) that this will have no impact on the reaction.