For salary or wage payments, kind of. If you received your normal wages in XMR then the government would have a hard time proving anything illegal is happening, even if both your employer and you are breaking the law.
People keep walking this back to massive fraud but more likely what anonymity will do is just allow businesses to escape onerous operating issues. E.g. having employees in some states is worse than having them in others because of those state's perceived requirements to operate an LLC in that state, and other related rules. It's not even clear if some of these requirements are enforceable federally.
As I mentioned, there are more defensible reasons for only having one party lie, like avoiding CA's (future?) claim that paying someone who lives in California implies you hired them in California and need to incorporate in California.