Yes - since I knew beforehand of the numerous bugs in Vault 81 (from the wiki) I did it yesterday without problems - I just wanted Curie as a follower.
If you never were in Vault 81, do this:
1) Use the switch to open the door. I won't open, but you have a dialog. There is an option to sweet talk your way into the Vault. Don't do this even if you can!!! It will trigger a nasty bug, which will disable your VATS and will not let you into the Vault. Agree to pay 3 fusion cores. (In the first quest you will get one back). Talk to the overseer and enter the Vault.
2) Important! If you see a gray cat named Ashes running by you - this is good, ignore the cat.
3) Walk further in and look around as much as you want. Talk to the two named NPCs in the entry area.After using the elevator you arrive in the Atrium. There a boy will ask you to take a tour and he will ask 5 caps. Agree, follow him, ask him what you want and wait until the tour ends. It is not long anyway and you get to know several people.
4) At the end of the tour the boy will introduce you to his girlfriend Erin. After this the tour ends. Now talk to Erin - she will tell you about her cat, which escaped. She will ask you to look for her, since nobody in the Vault is willing to follow her outside. Agree to this, and go outside. The cat is near the Vault and near the small lake. Got to the cat and send her home. She will set off immediately. Follow her back into the Vault, take your time a bit. The mini quest says talk to Erin. Do this, the cat should be nearby. If you did not ask for a reward beforehand you will receive a fusion core.
5) Next go to the Clinic, and see Dr.Forsythe. He will ask to take a blood sample from you. Let him.
These actions trigger the next quest. Forget the collect quests from Calvin and Dr.Peske. They do not work well. But the two small things above trigger the main quest. You can look around in the Vault a bit, but do not enter the Reactor room!
After this leave the Vault and do something else. It takes 24 hours or more for the next quest to start. So return to the Vault after some days.
If you go down to the Clinic, you should see Dr.Peske and Dr.Forsythe arguing - this is the quest in the Hidden Vault, where you need to find a cure for the molerat virus. At the end of two fairly small levels with a lot of molerats you will find the cure and Curie. (Do not forget to look around in the room where Curie is).
And it is possible to come through, kill all the molerats and not become infected. Hard, but possible, without cheating. I had to reload 3-5 times under way but it is possible. (Level 36, used Mines, Frag Grenades and my trusty Combat Rifle (semi automatic)). For lower level characters it will be much harder, since you have no weapon to one shot kill the darn rats. If you wish to try, prepare chems to slow the time and use VATS. I never use VATS, because I have ludicrous low hit rates even in 5-10 meters distance. I hit much better and faster with direct shots. Depends on your perks and build.