No, they're fully working.
Lack of resources has no effect on Nukes and neither on Factories, Hydro- and Nuclear Plants. Also Forges and Stables keep working when the local resource is pillaged or the whole empire doesn't have any more. Marble wonder building bonus remains when the Marble is traded away, but does get lost if the tile isn't improved/pillaged.
Some random fact I can add here now because I learned it in the latest TSG:
A pillaged Maoi will not break the chain bonus for the others.