Undocumented and Organ Donor?

Consultation for ethics response pertains to a case in which a resident alien (documented) with end-stage renal failure, recently listed with UNOS for a deceased donor kidney transplant, presents to the kidney transplant program two or three potential living donors who are undocumented immigrants.

Question put to Ethics is: Ought the transplant program evaluate and accept undocumented persons as living donors of a kidney?
Note: This transplant program, and others asked, typically have not transplanted (recipient) undocumented persons. Public insurance apparently is not available without legal immigration status; although for a documented person/patient recipient of an organ, public insurance (or private, if they have it) is apt to pay medical expenses both for recipient and donor.

Are there nonetheless compelling moral grounds for not using as living donors persons without papers--or for doing so?