Yes, and that's an important point: The novel tells us that Vito kept Clem on a short leash, but allowed Tess to seem as if he were an independent operator, in part to keep his enemies in the dark about whether Tess was really part of Vito's armament. But, I believe Tess as a result developed an independent feeling that Clem may not have had. In the fish tank scene, it's Tess who starts the complaints. When Vito says, "Do you trust my judgment?", Clem says, "Always, Godfather," but Tess just hisses, "Yesss." And, when they leave the room, Tess gives the left-handed handshake--sure sign of impending treason.

That's why I think Tess would never have accepted being under Michael when he moved to Nevada--and why Tess's treason was a stroke of good luck for Michael.