However, AP would be advantage in vocal sight reading. With AP, you will never sing a wrong note, whereas a non-AP could make some mistakes, depending on how strong there musical ability/relative pitch is.
I am not sure shifting keys in singing would be hard for people with AP. Of course they would be aware of the exact new notes they would be singing whereas nonAP would simply thing "everything is X steps up/down" but relatively the same.
I don't think AP has an effect on tolerance to listening to a song in a different key, it is more your personal taste. I don't have AP, but I can tell when a song is in a different key from the original. I find it acceptable, so long as it is in tune. But I vastly prefer the original key simply due to familiarity. Also, some songs really do sound better in certain keys than others.