Can 4-aminophenol be used to produce 2,5-cyclohexadien-1-imine?
TL;DR

No

Explanation

As far as I understand, the reaction being suggested is as follows:



The first thing one should notice is that 2,5-Cyclohexadien-1-imine is not going to stay as it is. It will tautomerise to the more stable and aromatic aniline.


Let us go back to the starting material - 4-aminophenol. Both the oxygen and the nitrogen are directly attached to the aromatic $\pi$-system. Both can donate a lone pair and cause a +R effect. Their electronegativities would result in a -I effect, which is very small, compared to the +R effects. The point is, the starting material is electron-rich, i.e. nucleophilic. It would not leave a carbocation (if it does form) alone.

Also, the thing about the lack of a hydride donor...