Can a burn patient have an allogeniec skin graft without being put on lifetime immunosupressant...

Allogeneic Skin: Allogeneic skin grafts are invariably rejected in an acute fashion. While current immunosuppressive treatments are effective in preventing early rejection of organ transplants, such as kidney, they have little or no effect in skin transplantation.

Typically not: Usually, if it's not autologous skin (your own), your immune system will reject the skin, and it will begin to slough after about 3 weeks.