Is it possible to generate a high-poly spherical model from a mercator-projection heightmap?

I'm a complete noob in Unity, but I've got a few ideas. One of them entails creating a model of Mars with height incorporated into the actual model, so I can adjust the sea level dynamically.

Essentially, I want to make something like this

from a map like this

Is this possible? If it's not possible in Unity, are there programs out there that can do this same sort of thing. Manually modelling the surface would be an absolute pain.

Thanks in advance.