Actually what happens to Autumn is simpler than that. He merely walks to the door to the outside and stops.
If you're on PC, go to the exit of the Taft Tunnels and use the console to break in and go back through that way. You'll eventually come out at the Purifier. Only, this is the version of the purifier that exists for Take It Back!, not the one that exists in the normal wasteland. Do NOT go back into the rotunda, it will eventually explode. Head back towards the exit, you'll see him and his two guards, all friendly, just standing there.
I didn't try to engage in dialogue, so I'm not sure if that works or not.
That doesn't mean anything. That's just game mechanics -- you can't actually say that's what happened to Col Autumn.
In any case, I don't think we'll know until canon sources say something. Personally, I hope he survived -- Autumn is a great man, with the heart of a lion... the guy truly wants to restore America to greatness, but he goes about it realistically. If he became president, the USA would have been reborn. Hmmmm...
I always let him live.