TGIE will not be able to affect Lama Gangchen very much. Lama Gangchen is very smart... not necessary the UN will back him up but so long as TGIE is his enemy then China will be his friend and I think they will do alot to prevent Lama Gangchen from falling due to unfortunately political agendas.
However, Lama Gangchen has so many powerful sponsors from so many parts of the world, I am sure they will remain loyal and faithful to him and protect his movement and vision.
Lama Gangchen has survived this long and grown so huge, building monasteries even in Tibet... no way TGIE can ever bring him down no way. If I was them I'd befriend Lama Gangchen. Perhaps TGIE needs his help to lias with China or open some kind of dialog, perhaps?