No. Not all energy in the oceans cause waves.
Let's say you magically dampen all of the surface waves... there will still be plenty of energy in the ocean, which eventually will cause the surface to move.
As a simplified example, the Atlantic currents are really strong, moving in a figure of eight between south America and scandinavia. However, most of it happens near the ocean bottom.
In some spots near the coast of Brazil this current is strong enough to cause anchored surface buoys to have wakes, while it can be perfectly calm a few km away. But the currents are still there, just much much deeper. The amount of energy involved in this Atlantic dynamo is extreme.
Source: Trying to accurately position subsea sensors at 1800 meters depth in the Campos basin is fucking annoying. The subsurface currents go in different directions based on how high in the water column you're measuring. I have seen these cables hanging from ship to seabed, and the transponders show it being pulled in wildly different directions at various depths. It was common to see it diverge several hundred meters in two or three directions along its length at the same time - It was like trying to accurately position a 1800m long {