Unity terrains can't be rotated, so no. You have to do your own spherical terrain system.

I would say that it wasn't impossible with 6 faces but there would be no way of projecting the edges at an angle - so I think it would always look odd. More faces though and it might work.

You'd need an algorithm to map a 3d point onto a face and an x,y coordinate for that face, then project the Z to the height of the terrain at that location.

So you'd need to calculate the point of intersection of the face's plane from a ray projected from the centre of the virtual sphere, then get the angle of the ray to the plane. Using trig you know that the point on the plane which needs the height is a perpendicular (it's angle will be 90), you know the angle of intersection so you can figure out the point that it touches the plane. You also know the distance from the plane - so that is the height for that point on the terrain.

Now clearly you'd want to plot a few spherical points and interpolate the heights between them. on each face. Giving extra consideration to the joins.

I guess you could also distort by a sphere as well, just adding your smoothed 3d heights to the existing height might make it look interesting.

Anyway just a thought. No idea what performance would be like :)

i made something like what you are trying to do its pretty simple acually and need no modeling skills thanks to youtube i used blender to model a sphere and used the noise button a few times then morphed the sides of the sphere to match the top there are plenty of toturials out there to follow in the end it looks like mountains and all you got to do is uv map it be sure to uv map before you subdivid or blender will freeze trying to map out with all the verticies and bumps hope this helps.