Overlooking that we are comparing the richest EU state to all 50 US states, doesn't that further the point that having unions is are at best uninfluential.
Either way, no, if unions don't reduce how much people make and provide stronger worker's rights, protection from corporate abuse, workplace safety, collective bargaining for things like holidays, you can think it doesn't change your take-home at all and pretty undeniably see the benefits. How many weeks of legally mandated paid time off do you get, and how many additional days do you get on top of that as a median worker in the US? :b
For comparison: unions are at best toothless in Singapore, there's no minimum wage, yet we have some of the highest wages in the world.