The short answer is no. There are numerous laws against hiring illegal immigrants or anyone without the proper work authorization documents. In an effort to curtail the hiring of illegal immigrants, these laws require that any employer obtain proof that an applicant can work in the United States.
The types of proof required vary from birth certificates, social security cards, or passports, to legal immigration documents such as a green card or work visa. Any place of employment that does hire illegal immigrants, whether by ignoring or failing to comply with regulations requiring proof of work authorization, faces legal consequences including fines or criminal charges.