First, your undocumented status could be revealed during the litigation of your claim. Eventually, the INS could possibly investigate and deport the worker. Although this is unlikely, it is still a possibility.
Second, often wages are paid under the table and paid in cash. Because of this, and the worker's undocumented status, many times these wages are not reported to the IRS. Again, although it is unlikely, the IRS could investigate.
Third, the employer is less likely to bring you back to work after you recover from your work injury if he discovers during the litigation of your compensation claim that you are undocumented. However, most likely the employer already knows your undocumented status before the work injury. Further, if the injury is serious enough, you might not be able to return back to heavy labor work anyway.
The bottom line is that if you're an undocumented worker and are injured at work, before you do anything you should talk to an experienced workers' compensation lawyer.