I've tried this a few times, and it can definitely work. The biggest problem I've had with it is that Elephants are pretty expensive to build. So it takes awhile to accumulate enough of them to start your attack, and if you're unlucky and lose one or two your offensive quickly grinds to a halt. And while they're effective at guarding newly captured cities, their high cost makes this inefficient.
All in all, I think this is a reasonably effective strategy but one I'll only follow if I can't take the more conventional route of killing people with Axemen or Swordsmen. Those units are cheaper to research and build and with the right promotions are almost as strong as Elephants. More units allows for greater flexibility, plus once you get Macemen they can be upgraded and become even better than Elephants. Whereas Elephants don't get an upgrade possibility until Gunships.