I disagree with the other answers. The plate will be warmed, but not enough to shatter.
First, I assume that you are talking porcelain plates. Glass (or Luminarc, etc.) is another matter. Porcelain is much more heat shock resistant.
Second, while the metal has both a higher heat capacity and a higher mass than food (as Jefromi mentioned in his comment), it also has a much higher heat conductivity than food (80 W/(m.K) for iron, 0.58 for water, and food is mostly water) which means that it loses heat quicker than food, not slower.
Third, look at the shape of the gas burner. Unlike a resistive electrical stove, you don't put the plate on a heated plane surface. There is a metal grid which supports the plate. Yes, its bars are hot. But they are small and thin, and sit in the air. Which means that, due to their shape, they lose their heat quickly.
Fourth, look at the plate from below. All plates I have seen have a small rim on the underside. This means that you don't even have the whole metal bars come into contact with the plate (which still wouldn't have been too bad); the only part you get heat exchange are the small points where the plate rim touches the bars.
Take all this together, and you see that the heat transfer is very small. A broken plate can't be completely ruled out, but based solely on the strength of the thermal shock, the chance for it happening is way below the chance of a room-temperature porcelain teapot shattering when somebody pours boiling water into it. And people do that all the time, so I would see it as an acceptable risk level. (My urge to tell them to preheat their pot for better tea notwithstanding).