Documented immigrants will get a ITIN and/or EIN.
Undocumented immigrants are far more likely to go the... undocumented route.
Undocumented immigrants are far more likely to go the... undocumented route.
In terms of immigration, undocumented typically means you don't currently have a valid visa or residency permit. In that case no, they would still be undocumented, since the ITIN doesn't grant them either.