It doesn't work for built in meshes. Needs to be an imported mesh, that I also save as a Godot .mesh.
Reference links: Facebook, Mesh Data Tool, Mesh Class
I was mistaking pointing to Mesh class instead of mesh attribute to get the mesh reference. And the if test needs to check pass, because "createfromsurface()" returns a non zero when an error occours.
var themesh = mesh # Same as bellow, points to same object in memory
var themesh2 = self.get_mesh() # Same as above, points to same object in memory
print("Mesh surface count: " + str(themesh.get_surface_count()))
var mdt = MeshDataTool.new()
if mdt.create_from_surface(themesh, 0) == OK: # Check pass
var aMeshVerts = 
for i in range(mdt.get_vertex_count()):
aMeshVerts.append(mdt.get_vertex(i)) # Storing the vertices positions
mdt.set_vertex(0, Vector3(1, 2, 1)) # Changing a vertice position