The simple answer is no. However, in the real world, the answer is more complicated.
There are federal protections that protect employees against employer discrimination when employers have 15 or more employees. These protections apply to every employee, not just those who have authorization to work.
Your employer cannot use your lack of immigration status as a way to evade the anti-discrimination laws. For example, the employer cannot fire you because of your religion. The law specifically bars employers from firing you for certain reasons. You can find a list of those reasons here.
You are still in a difficult position. If your employer reports you to Immigration and Customs Enforcement (ICE). Even though the employer’s actions were illegal ICE is allowed to follow up on the employer’s report. If ICE does follow up, it can try to deport you.
It’s worth noting that immigration laws obligate employers to document that you have authorization to work in the U.S. If you are not authorized to work, and ICE discovers your employer knows it, then your employer could be in trouble.
You can see that both sides face certain risks if employers violate labor laws. There are no “yes or no” answers about this issue.
Laws about employee rights and employer obligations are not simple for employees without authorization to work. That’s why it’s best to consult an immigration lawyer about your situation. Landerholm Immigration can help you sort through the facts and advise you.