Pretty much. You're only doing a free and willing exchange when you have an alternative. Otherwise by definition, there is no choice. Not that this means employers are slavers, it's the system that enslaves people, but employers gladly take advantage of it.
Edit: downvoting without discussion in this context means to me that you're hurt by my statements but have no rebuttal. It feels like you're acknowledging what I'm saying as true but you're not happy about it.
I don't think having alternatives is the criterion for a free choice.
The problem with "free" is like one of the other commentators suggests. If you get two guys offering the same terrible deal, you're no better off, but the critic can tell you you had a choice. And it's turtles all the way down, package the choices as one and the critic will tell you to unbundle them.
Instead we have to look at cultural context. What people think is reasonable changes. At one point, people thought it was just fine that if you couldn't pay your debts, you had to work it off, and your kids would inherit that debt. We also thought it was just fine to let kids work in mines, and that labourers should work every day minus Sunday.
"Whatever you can get someone to shake hands on" (which someone else is essentially saying) is another one of those ideas that seems simple, but actually there are social constraints on what you can agree. It's inviting to pretend that whatever the person agrees to is free, but actually this isn't the case and historically hasn't been.
Edit: downvoting without discussion in this context means to me that you're hurt by my statements but have no rebuttal. It feels like you're acknowledging what I'm saying as true but you're not happy about it.