General answer: No.
Specifically, Labor Code 3551(a) states that "aliens" are employees for workers compensation benefits. The term 'alien' refers to a person who is not a US citizen. They may be classified as documented or undocumented, with 'documented' permitted to work in the United States by having a 'green card'.
The Labor Code does not distinguish between the two when it comes to documented vs. not. Both the Labor Code and case law does not require someone to be a citizen to get workers compensation benefits. Gutierrez, dba Armstrong Co. v. WCAB (Flores) (1976) 41 CCC 184 (writ denied). See also Dittman v. Knapp, Allison (1943) 8 CCC 189 (panel decision) (enemy alien was entitled to benefits); Alfaro v. WCAB (Mier) (2001) 66 CCC 1 (writ denied) (Court of Appeal opinion unpublished in official reports) (undocumented worker was awarded benefits)
Read more: Do I Have To Be A Citizen To Get Workers Compensation Benefits?