MAKES YOU THINK THAT THERE COULD BE A SYNTH VERSION OF EVERYONE FROZEN IN VAULT 111. THAT WOULD BE AN INTERESTING DLC, A "LONESOME ROAD" ESQUE EXPANSION WHERE YOU TRACK DOWN THE SYNTHS THAT TOOK THE FORMS OF YOUR FRIENDS AND FAMILY EVENTUALLY LEADING TO A CONFRONTATION WITH SYNTH YOU
While this sounds interesting (and Gaben knows I loved lonesome road), it seems highly unlikely. There would be no reason to make a synth copy of anyone from vault 111, with the possible exception of the player, because we need more psychotic killing machines running around. Also, keep in mind that depending on your faction choice, the synth making machines are a radioactive crater underwater.
My hope is that the DLC for Fallout 4 plays out like Fallout new vegas: the base game was a little dull, but the DLC was spectacular.
I don't really think it would be unlikely at all. Shaun did make a synth copy of himself after all. It's only reason for existence was just one of his whims. The creation of other copies, then would be just as likely (although he would probably have to guess their personalities).
In the case of the fate of the Institute, the only real difference would be how the DLC is introduced.
If you sided the Institute, it could be you being sent to hunt them down because they escaped. The story can give you another look at the synths as you find these clones of people you once knew trying to survive without any knowledge of the wastes like you and Valentine did.
If you destroyed the Institute, you could have someone Preston tell you about some synths causing trouble somewhere and you have to go solve it.
Seeing as how FO4 was just basically everyone reacting to the synths being sentient, the real purpose of the DLC would be that it shows how the synths could possibly gain sentience and its implications in the post-apocalyptic world. The computers in the Railroad HQ show that some of the synths they memory-wiped became raiders, so it could focus on the moments like that when giving something freedom goes wrong.
For a less synth-focused quest line (and probably, more boring), they could just be used like in that one Mass Effect DLC, where your clone is trying to replace you.
IMO, though, FO4's story was already pretty weak and a DLC based off of it would have to lug that weight with it. Also, I'm pretty sure Bethesda wouldn't see any point in making DLC focused on synths when that was what the main game was about anyway.
TL;DR - I agree, it is unlikely, but I also disagree because I think it's not for the reason you said.
Well, no shame in two intelligent people reaching the same conclusion by different means. But more than this theoretical DLC, i want to see either something like Dead Money again, or something with more underwater. I loved dead money, and i spent two hours wandering around the ocean floor in power armor and eating mirelurk cakes. I was getting nervous that the game would say "OK, you've had you head in a bucket of water for the past two hours, now die horribly and go help another settlement."
I like the theory of Vault-Tec causing the nukes to fall. Seeing the massive capitalism that takes place in FO's pre-war lore, I wouldn't cross that theory off the list.