Absolutely not. Although urinating does elicit the parasympathetic nervous system, the sympathetic nervous system is still activated when you have to perform in front of an audience when you have stage fright. The activation of the sympathetic nervous system from fear is also known as the fight or flight response. It is not sufficient to just increase the parasympathetic response...you need to address why the fight or flight response is triggered.
With this in mind, the best way to cure stage fright is to engage in CBT (cognitive behavioral therapy). The following video explains how stage fright develops, and how CBT can help:
