Yes. This is an experimental technique for treating automimmune diseases.
What's more surprising is that you don't need a donor. You can take the patient's own stem cells, store them, and then retransplant them after destroying the immune system with massive dose chemotherapyy.
It seems that many automimmune diseases seem to occur because the immune system 'learns' that certain parts of the body are nasty invaders. With the immune system destroyed, the memory is lost, and when the stem cells are reimplanted and the immune system grows back, it no longer has the tendency to attack the body again. The concern is that the disease may recur, but this doesn't appear to be that common, such that the technique is regarded as an acceptable option for extremely severe autoimmune disease.
The self-transplant (or autograft) is much less nasty than a donor transplant. An autograft only carries a fatality rate of around 5-10%, whereas a donor transplant is in the 25-50% range. This is due to 2 major problems - with a donor transplant, you have to be absolutely certain you've completely killed the host immune system, otherwise it will reject the transplant (so much higher doses of chemotherapy), and 2nd you've got the risk of graft-vs-host disease where the transplant rejects the body - even without GVHD, a donor transplant still requires very high dose immune suppression drugs for life.