There's nothing funny about the act of drunk driving. There's also nothing funny about plane crashes, terrorist bombings, married heads of states getting sexual with young assistants, heart attacks, or dying. But the DISCUSSION of these and other serious concerns of life need not be limited to the grim, stern, matter-of-fact approach. Expressions of humor help balance our outlook on life, and are necessary for good mental health. A light-hearted treatment of a topic is often an excellent alternative or complement to a straightforward one; in some cases, a joking statement can be much more effective in showing absurdities and making the point than a somber one. In a nutshell--lighten up! (Said with a friendly smile)

The song in question is not so much funny (your word, not mine) as clever. I think it would do a good job of raising awareness of the problem in those who heard it, without risking a defiant reaction by being preachy, boring, etc.