Yes, HIV targets mostly Helper Tcells, you still have quite a bit of immune system left even after you have AIDS that could kill the transplant. So you would need to take immunosuppressants.

That being said the question most of the other comments seem more interested in would be if someone with AIDS would be a candidate, and I think a lot of the answers people are coming up with are flawed.

If someone happened to be in liver/kidney failure and it was somehow discovered that they had also had undiagnosed HIV/AIDS or an AIDS defining infection, they would unlikely be a candidate for transplant until their concomitant infections were resolved and they were undetactable and showing some improvement with cd4 count, if they survive to that point they would potentially get listed and potentially get a transplant, especially from an HIV positive donor.

In the US at least, we are pretty good about screening and catching HIV infections so that people live with the virus for a long time.