Where does this come from? It seems to have two problems since not only does the plural "they" not agree with the singular subject "whoever", but it switches from using the singular "is" to the plural "are". I dunno, I don't buy it. Perhaps it isn't technically wrong, but it's definitely frowned upon.
Alright I suppose I have to concede that point seeing as the OED says the same thing about they being used to refer to a singular noun of unknown gender. I guess it's only frowned upon in formal writing.