Can you get an adult cottontail that is used to captivity? Even for wild european rabbits confinement is huge stress,
I don't know much about cottontail behaviour, like, are they social animals like rabbits, or solitary like hares? From the little I know that wouldn't be a natural situation, right?
I can only tell what my rabbits do when encountering kits they are not used to accidentially, which is chasing them away. Didn't make much difference to adults, but that kits were about 8-10 weeks then.
My buck, on the other hand, is super friendly with any kit that ventures into his realm, his spayed cuddlebun not so much.
I keep breeding does in pairs, but only once I got the impression that the second doe in the hutch, that didn't have a litter herself, started to nurse the kits of the other doe when they came out of the nest and tried it, but I can't tell for sure if they actually got milk from her, I guess so because they kept doing it for quite some time. Rare occurance, and in a stress free, familiar setting.
The second does are great stepmothers though, and the kits grow into that herd without any trouble, but nurturing other kits spontaniously - not really.
I guess it's much less likely with cottontails that don't live together in warrens.
I would ask rehabers with experience on that, I think there are no useful conclusions to draw from domestic rabbit behaviour.
Intuitvely, I don't think it would be worth the risk.