Doesn’t this discussion treat supply and demand as material phenomena rather than the derived numbers that they are? Equilibrium is where supply and demand meet. Wherever that may be, supply and demand have met. If we mistake quantity for supply, we are making a semantic mistake. It doesn’t matter how many employees there are. If they are unionized, the supply curve of labor — the graph of how many workers can be had for a given price — may take on a very odd shape, but if a deal is made, supply and demand have met.
The argument that employers have more power than employees assumes that the employees compete with each other while the shareholders of a company bargain collectively. Unions even that playing field, as does legislation (another form of collective bargaining). I prefer to think in terms of how arrangements like cartels, unions, and governments affect the curves than to say that the curves derived from unspoken assumptions (e.g. non-unionized employees without legal protection) don’t describe the economy.