The drunken boxing style exists in real life, originating from China. In Chinese it is called Zui Quan (sometimes called Zuijuquan). But unlike in the movie, it is dangerous to perform the art whilst drunk because serious injuries can occur.
There is a clip (possibly a teaser or a deleted scene) in which Wong Fei-Hung demonstrates drunken boxing on the front lawn of Beggar So's home; the latter calls instructions throughout, with characters subsequently appearing on-screen. It appeared in the documentary "Cinema of Vengeance" and later as a "deleted scene" on some home video releases.
A photograph from this (Fei-Hung with his leg raised, holding both a tea cup and wine jar) is commonly used in various artworks.