Yes, and if they didn't, a court, made up of a jury of their peers, would find the contract void, as contracts require informed/genuine consent.
>>If there's only one employer in town (or a range of employers offering the same conditions), then that freedom is moot.
Even in the late 19th century, workers in company towns had market options:
https://marginalrevolution.com/marginalrevolution/2015/01/in...
And in any case, that situation is exceedingly rare, especially in the modern highly urbanized economy, where a large and growing percentage of the population lives in high population metropolises with thousands of employers.
>>There needs to be equal forces pushing up and down on workers' rights.
I disagree with this assessment, based on the empirical evidence, which shows wages consistently rise in lockstep with per capita GDP. What gives workers bargaining power is companies seeing their productivity and revenue rise, and as a consequence, bidding more for workers' services as they compete with other employers. That's the dynamic behind wages in China tripling over the last twenty years.