It won't stop, it'll just ruin your rep. with the faceless. Use the tchortists as meatshields, and keep them away with your force field, don't kill any. Just run to that elevator and shout at them all : "Screw ya, suckers!"
You won't be able to get back into the Institute. And you won't be able to get back to Underrail for some time, you are locked in the deep caverns. So pack up on supplies before Eidin starts the elevator. It's a point of no return.
In the DC, it's pretty useful if you have a good rep with the faceless. If they are hostile towards you, you have to watch out for patrols and assasins in the south-eastern half of DC. And the north western half is populated by horrible creatures. So...don't ruin your rep with them. Complete their 3 quests. (Tell them that their item is in Corecity. [Foundry]) (Free the captured faceless in Corecity and give him a healthhypo. [He is in the deep Dropzone]) (Last but not least, allow the faceless in Buzzer's shop to read your mind.)
You'll have 3 rep points then. If you kill a certrain ammount of faceless you loose 1 point.
You need at least 2 rep points for supplies and safety in the south eastern half of DC. If you manage to reach their commander with 3 you'll get a lot more lore from him.