I absolutely do this. I have plenty of songs on my ipod that I enjoy maybe three seconds of.
One of my favorite songs from the last few years is MGMT's Time To Pretend. It's a fun pop song about being a rock star that sounds like a parody but works even better if it you assume it's meant unironically, which it apparently is.
Although you kind of need to hear the whole thing for it to really work, the best part of the song starts at 2:13, with the overly whistful verse about all the things that they'll miss once they become big stars. And the "moment" comes at about 2:28, with the incredibly over the top return of the drum machine.
It's completely ridiculous and should ruin any sincerity the song has, but somehow it woks perfectly.