Yes, I have alwayd doubted it is a parody, at least partly, but parody or not, that doesn't make any difference. See, whilst listening to it, I don't see anything funny in it, no, to me it sounds perfectly like some obnoxious vulgar lyrics that weren't meant to be a joke at all, for example like those that Kiss used to write.
And if one doesn't get the joke without knowing the context, it doesn't really work, and many people seem to take it seriously which actually is kinda alarming. Parody, or not, I dislike the lyrics. It could work without that one line as well and still fulfill that purpose you talked about.