Is the neutral outside of the plug dangerous while carrying current?
First of all, you cannot be sure that the stem is connected to the neutral wire and not to the live one unless you test it with a testing screwdriver, since alternating current is bidirectional.

Even if we consider it to be the neutral one you cannot trust that it is safe to touch. In ideal circumstances, where the neutral wire is very well grounded, it shouldn't have an electric potential. However, if there is any problem with the wiring or grounding, now or in the future, it could be dangerous, if touched. 

I would suggest to cover it with some insulating tape.