When you meet Mobius, he explains that the Think Tank brains want to transplant themselves into bodies, after which they'll be able to leave Big Mt. Does this mean if you choose to put your brain back in you can walk outside the perimeter without getting teleported back? Or does the perimeter always work? From exploring, I know you still get the perimeter warning after the main quest without your brain, so just wondering if your brain lets you explore further afield.

Nope, you still get teleported away after a little delay.