I think he can use his breath underwater, but I don't think he will.
@Druzilla54, I've heard that Edwards wanted to give the breath a realistic makeover, but I honestly doubt he changed that much. While it will be different, I'm convinced that it will still be the standard beam of complete destruction. Especially after Zilla's poor excuse for a breath attack (you know, exploding cars instead of actually breathing fire), I doubt that he would chance anything extreme. I think he will want fans to clearly recongnize it as his signature attack. I see it as a very bright beam, that instantly destroys whatever it touches with a combination of vaporizing, melting, and exploding the target. Almost like a superintense lightbeam. Gareth made a huge point in his interview to say that this is not Godzilla 2014, this is what Gojira 1954 should have been. And Gojira's original atomic breath destroyed everything!
Going into what it would look like underwater, I would think it's going to look very much the same. The thing is, because it's underwater, the heat released from the beam and his spikes would instantly boil the water around them. Come to think of it, perhaps Godzilla's whole body would have a similar effect whenever he was underwater because of his own body heat. That would certainly look cool...