I've actually done it before, for my custom dragonman race and they don't actually need to sit on the egg 24/7 from my experience. But they also seem to stop laying fertile eggs after a few goes.
There's other issues too though.
Only married civ members will lay fertile eggs, but all female members will try to claim a nest box requiring personal rooms, and a lot of micromanaging.
*Set nest box to be built in a married couple's room
*Wait for a worker to deliver the nest box to the room
*Suspend construction of the nest box once the worker starts construction
*Wait for the female to enter the room, lock the door
*Unsuspend construction of the nest box
*Once the box is complete since the room female is the only one that can reach it she will claim it automatically.
Eggs will be heartlessly carried to the food stockpile after laying almost immediately, sometimes by the mother. They will no longer hatch if this happens, turn off all stockpiling of your race's eggs.
The original owner will usually reclaim the nest box once it becomes available again, but it's not guaranteed.
The mother immediately drops everything she is doing to go pick up the baby the instant it hatches, but if your fort has a lot of dangerous drops, she might not get there in time.
The mother will work normally but will spend idle time on the nest box instead of in meeting halls or partying.
As stated above the mothers will randomly become infertile, but I think that's something inherent to egg layers in general, not just civ egglayers.
As for what science I determined I have little except what I already mentioned. I know 100% that they don't need to be on the nest all the time, in fact that's how I know the mothers will drop everything they are doing to go pick up the baby, I've seen them hatch with the mother elsewhere. But I don't know exactly how much time must be spent on the nest, I've seen military moms crap out an egg and never come back and the egg successfully hatch, I've seen dedicated nurse moms that have no labors never leave their nest except to eat drink and sleep produce duds.