My take is that it would ignore the laws of economics to say that any change in the MW would have no effect on MW employment.
On the other hand, economics also recognizes the concept of demand elasticity -- the fact that for some goods a small change in price has a big effect on demand, while on others, a large change in price only has a small effect on demand.
The demand for low price labor seems to be fairly inelastic -- that is, an increase in the price of labor (e.g. the MW) has a moderately smaller effect on demand for low end labor.
Thus, for example, we have seen periods (e.g. the mid 1990s) of significant MW increases with little or no apparent effect on MW employment. However, there is certainly a level where the higher cost will have a greater effect on employment.
That would work if the economy was functioning normally, but say there is a fall in demand and workers are unemployed and factors stop production. Then there is a clear fall in demand and companies have to take cost cutting measures, at this point there are generally two options for employers cut wages, or cut jobs. At this point since the fact that the price of low end labour is inelastic doesn't matter as demand has fallen. This is where the minimum wage is a problem, it acts as a legal limit to wage cuts.