Persistent deep ocean currents exist in large part thanks to temperature gradients (cf. AMOC and thermohaline circulation). Climate warming, melting ice and reducing these gradients, has much more drastic effects on ocean currents (cf. Gulf Stream weakening) than a turbine could ever have.

Paradoxically, we would effectively be saving those currents using a fraction of the energy in those currents themselves.

Using these turbines would be a drop in the ocean and a smart move if it helps us tackle the big offender. We should get on it soon though, if we let it get to a point where thermohaline circulation falls apart using currents this way may no longer be an option.