Salary transparency already exists, just that it works one way only: the employer knows everyone's salary and they thoroughly research the salaries paid by their competitors.

As a general economic principle, I can't really see any situation where this information asymmetry works to the benefit of the workers. It might benefit some employees in critical positions that can bridge the information gap and gain an advantage over their peers.

But on average, no, transparency reduces the leverage of the employer; else they wouldn't fight to maintain that information differential, they would promote full transparency in order to pay everyone less as you say.