They'd operate more predictably than they do on non-tidally-locked worlds
(The following to be spoken in your best Rod Serling voice...)
Imagine if you will1 a ball, held in place in front of a hair dryer with a block of ice behind it. You observe that water is on the surface of the ball and the heat from the hair dryer causes the warming water to expand, resulting in convective currents flowing to the back side of the ball, where the water is cooled by the ice. As the water pressure on the backside of the ball increases, water is forced back to the side with the hair dryer. You realize, to your horror, that the result looks suspiciously like currents.
You have a water world, so it's going to have gyers centered on the solar terminator. Heated water from the sun-side pushed toward the opposite-side. Cooled water pushes back.
Now, it's highly unlikely that your plant's non-water surface (you know, the ground beneath your keel) is smooth as a billiard ball. So, unless the water is always fairly deep, the undersea geography will cause more interesting currents. At a guess (and I'll admit, it's a bit of a guess on my part), shallower areas will tend to provide the channel for hot-to-cold currents while deeper areas will provide the cold-to-hot return.
So, while your oceanic currents would be much simpler than you'd find on a rotating planet with land, I don't think they'd be boring.
Just in case you were wondering, I'd expect that wind would basically do the same thing — but with complications. Evaporative moisture is part of the mix, meaning you'll have some honking massive storms at the terminator. I'm also ignoring things like ice at the poles, which will complicate both the currents and the wind. And I'm definitely avoiding clouds. But if you're to consider them, that's all to your good, right? Because they just add complexity to the equation.
1 Rod Serling never actually said the phrase, "imagine if you will." But pretty much everyone who hears the phrase today hears it in Rod Serling's voice. You go Rod!