No. Graft vs. Host disease is when a bone marrow transplant patient's new immune system doesn't recognize that patient's organs and attacks them. It is effectively an autoimmune disease and it is in no way contagious.
I am a survivor of both NH Lymphoma and AL Leukemia. I had a bone marrow transplant in November of 2011. My sister was my donor and a perfect match. Six months post transplant I developed chronic GVHD. I have lost range of movement in my knee...