No.

If you look in the instructions for any range they'll say how far anything flammable has to be. The very least above an open flame is 30". It might be more for a Bluestar, which is very powerful.

Usually shelves over ranges are made out of stainless steel. Stone or tile might be okay, but probably won't pass code if there's wood underneath. If it's molded ceramic or carved stone, it might be okay.

Do be aware that any shelf over your range like that is going to interfere with the draw of your hood, and will be dangerous to use due to reaching across hot, and possibly scalding pots, and potentially hot enough fire to catch your sleeve. Additionally, anything you put up there is going to be heated, so it's a poor place to keep any kind of seasonings and spices. The "look" dates back to when people didn't have countertops next to their ranges and was a place to stash pots coming off the flame, and bowls of rising dough, like the shelves in the sides of the old open hearths.

That's just a caution. If you want it, there's no reason not to do it, so long as it can't combust.