I don't think so, I think they just didn't realise Autumn was 'throwing Eden out of office'.
There is absolutely nothing to suggest that, not only do you admit that Eden has built a very successful cult-of-personality around himself (with some Enclave Troopers last words being "For Eden...") but also Raven Rock is entirely under his constant visual and audio supervision; you think that Autumn could possibly organise any kind of secret uprising there? Not only that but when your talking to Eden his wording suggests that this is the first overt action that Autumn has taken against him ("Now that he's
openly countermanding my orders") and I can't accept that anykind of largel popular resistance with Raven Rock of all places could take place.
It makes so much more sense that Autumn simply used the popular consensus to his own ends to combat the perceived threat that the Lone Wanderer presented, what-ever that was (baring in mind that Autumn was sincerely of the belief that Eden had abandonned the Project); who knows actually, combined with his denial at the Purifier that Eden would ever betray him, his defence that he's operating in the chain-of-command maybe he did what he did thinking that he was
helping Eden; it seems clear from the Purifier that he never considers his actions as a hostilities against Eden.
“Eden betrayed you. See this vial? He trusts me more than he trusts you.”“That’s not true. That plan was abandoned months ago. He would never go behind my back!”“But you know he has. He sent me to do a job that you wouldn’t.”“You could have stolen the vial… it means nothing. It proves nothing.”“Why are you doing this? Why give your allegiance to a machine?”“I am sworn to protect the Presidency. The chain of command must be upheld. I wouldn’t expect you to understand.”In-fact yeah it makes total sense, he either thought that the Lone Wanderer was going to take his place with Eden or that Eden himself had been fooled into trusting the Lone Wanderer whom in reality presented a threat.
I'm prone to sentiment for Autumn, even giving mercy to him at the Purifier. But ultimately, Autumn is overly idealising the Enclave. The idea of the Enclave EVER coexisiting peacefully with 'Wasteland Trash' is laughable because the Enclave is a racist organisation, judging others based on their genetic structure. He's chasing a pipe dreaming that would never be because the Enclave's naive 'purity' is their version of the Codex, an outdated concept impeding their progress. Look at the Enclave integrators in New Vegas, they've survived in the wastes and surivived just fine. Maybe the world isnt perfect, but it IS livable for 'Pure Strains'.
Quite frankly Autumn started the chain-of-events that got everyone in Raven Rock killed, everyone under his command at the Purifier killed and then he gets the chance to walk away?
“You’ve already won. Allow me to leave with some dignity.”[censored] off Autumn, you don't get any dignity you imcompetant, selfish [censored].