Hello! You can, on ASE, pick the screen depth, and through that you can do some math on the objects distance to what is behind it, but this might be a bit different from what you want. You can also use depth fade, but this is not something that's on the shared references, it's belongs to a different technique.
The mesh blending example you've shared is based on the Distance Fields functionality in Unreal 4, which samples the level global distance field ( which is automatically calculated by the engine ), and is something we don't have access in ASE. In Unity you would likely need to precompute the distance fields outside the shader and then feed them into it.
In any case, this is a fairly complex effect that will require some elements external to our editor in order for it to be achieved. Unfortunately, we don't have any immediate advice or samples that we can provide, so for now I would recommend that you look into a package that would specifically solve this problem, such as
Terrain Mesh Blending, or even
Micro Splat.
On a final note, an alternate way to simulate blending would be to use world projected textures on both the terrain and your mesh, however, this is not an ideal solution and it differs from the other technique.
Hope this helps!