Undocumented immigrants can get an ITIN, and many do. A lot of the time the ITIN will be used where it's allowed (opening bank accounts) and a counterfeit social security card where it's not (applying for employment).
I guess in a pedantic manner, but then they were always documented, since their country of origin knew who they are.
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.