Nope.

Klippen said food safety is paramount and refutes claims that cage-free housing improves egg safety. Pennsylvania State University researchers have found that eggs from small flocks of chickens are more likely to be contaminated with Salmonella enteritidis as eggs sold in grocery stores, which typically come from larger flocks. The analysis of the S. enteritidis present in the eggs from small flocks shows that they are the same types commonly reported to the Centers for Disease Control & Prevention from human foodborne outbreaks.

https://www.feedstuffs.com/news/michigan-governor-vetoes-cage-free-egg-bill