It's a good, if imperfect, analogy.

Slaves were indeed forced to work at swordpoint, and under threat of corporal punishment. Wage slaves are not. Instead, they are forced to work under threat of starvation. There is certainly a difference, but it is not one that amounts to freedom.

And even a wage-slave's employer doesn't have "infinite" influence on the work, infinity being an impossibility under any practical conditions. A wage-slave's influence is marginal to insignificant, except in professional practice.