We've had entire boars slaughtered without any taint - but to be fair, they were young and in a batchelor group.
There's been threads on this before and the general opinion on boars was that so long as they were away from females for a period before slaughter, they were fine.
Can't say anything about billys as I have no experience but we sent our tup away in March time and he was fine. He hadn't been near any ewes since the December.