Yes, it is possible. This texture wasn’t designed with that in mind, but you might be able to make it work. What you need is something in the texture that all the gold parts have and none of the other parts do. Once you have that component, you can turn it into a zero to one factor, and drive the Principled BSDF’s Metallic input with it.
So, what's something unique about the gold patches? Well, everything else in the image is greyscale (white and grey marble), but the gold parts are colorful orange. That's our way in. The colory-ness of an image is also known as its "saturation." Using a Separate Color node set to Hue-Saturation-Value mode (or HSV), we can get the saturation channel. I've temporarily plugged it into the Principled BSDF's Color input so you can see what that channel looks like:
Notice how the gold parts are white and everything else is much darker. But, the other parts should be black: The Metallic effect on them needs to be zero. So, we need to map this slightly-higher-than-zero to one range to an actual-zero to one range. We can do this with a Map Range node:
I've set the From Min input of the Map Range node to 0.1, slightly-higher-than-zero. And voila! Our Metallic effect map. Now, we just plug this into the Metallic input and put the color back:
Hope this helps!