It wont hurt to ask... maybe they can find you an appointment that's early so Delilah have time to wake up nicely, perhaps then they'll let her go when they see all is fine. I'm not sure how it works at the vet but I somehow strongly doubt there is a vet staying over night with the animals... or is it normally? I feel they'll be better off at home as long as they're not at any risk.
Boeboe has had a few ops as you know and the only one she got sick after was her spay, and that is not an operation they keep them over night after. She wasn't badly sick, she just threw up a few times but I was a nervous wreak She came right quite quickly though and she got boiled rice and chicken for a couple of days so she was happy
You were born with the ability to change someone's life, don't ever waste it.