Consequences of the Think Tank acquiring a Gen 3 Synth?

Big MT outclasses the Institute in every area aside from robotics. If the Think Tank got hold of a Gen 3 Synth, they could reverse engineer the tech and create Synth bodies to house their minds, ala "Surrogates". Since the Gen 3s use human DNA, all they would need is to use a few pieces of brain tissue and pictures of their old organic bodies to use as references, and there they go, walking out of Big MT.