I think you are stretching it too much.
My guess is that native English speakers are so over-exposed to the double entendres of those words that they no longer notice. I certainly didn't.
Yesterday I had too much time on my hands and I watched very closely the video for the song "When your heart is weak". The song is not that bad, but the video is pretty awful. There's one scene in the middle of the song, where the band are playing in the desert on a cliff or somerhing similar. I don't know what the singer is doing. I guess he's dancing, or at least he's trying to dance. But the lyrics go something like "I'm gonna come without warning". Cock singing about coming? That sounds funny.