I read a case study where a business' productivity went up 200% when employees were given unlimited vacation. Would productivity still increase if every company did it?

I doubt it.

I think the study is only of limited value, because "productivity" is not always easy to measure in every business situation.

The case you cite probably involved a white-collar business where work output was easily measureable (e.g. how many tax returns did you complete?) and where there was considerable time flexibility (e.g. if Joe Smith's tax return was promised by Friday afternoon, it doesn't much matter if it's done Wednesday night or Friday morning).

Under that scenario, I can see where giving employees essentially infinite freedom to manage their time ("Gee, I gotta take Susie to her doctor's appointment. OK, these tax returns can wait until later") would make them significantly more productive.

That scenario may not translate to sandwich makers, garbage collectors, Wal-mart greeters, etc.