Ordinary waves travelling through the ocean, mostly yes. But when 2 Tsunamis crash into each other, you can bet, that there is lots of turbulence and energy lost and they wont have the same height afterwards.
I think you're imagining two towering waves crashing into each other. But in fact tsunamis only pile up like that when they enter shallow water. In the open ocean a tsunami is a wide area (~100km) of slightly raised (~1m) water. If two overlapped it would just be raised twice as high, which wouldn't cause much turbulence.
