The interesting question is NOT, "Does neck wood affect tone?" Everything affects tone. (Butterfly effect). The interesting question is whether you or anybody else can hear the difference that is due ONLY to the neck wood.

I personally have never noticed any differences that I would attribute solely to the neck wood.

There's lots more to the neck than just wood. Tuning machines, reinforcing rods, frets, fingerboard, finish, etc. I would expect their combined effects to far outweight that of the wood.

If there were a consistent difference audible to ordinary banjo players I would assume that nobody would have to ask the question.