I am not an expert in this, but I would suspect they would not be the same, related to Feynman's famous story.
The movements of the fluids are not the same in the two cases.
I imagine a wall with the fan or turbine set in it.
One way the fan sucks fluid in from one side, decreasing the pressure near the opening on that side of the wall, and pushes fluid out the other side. Since the moved fluid has inertia, it tends to move into the fluid on the other side.
The other way the fluid pressure on one side of the wall is higher than on the other side. High-pressure fluid turns your turbine, and lower-pressure fluid moves into the fluid on the other side.
The fan turns the same direction. One way it's high-pressure fluid in front of the fan and low-pressure fluid behind it, the other way it's the other way around.
So I can imagine that this might make the aerodynamics not be the same.
But maybe that doesn't make any difference.
Now take away the wall. The fan is stationary compared to the fluid all around it, and it moves some fluid. The fluid behind it moves relative to the stationary fluid around it, it has a velocity away from the fan.
The turbine is surrounded by fluid that has a velocity. It slows some of the fluid, and the fluid behind it moves slower than the fluid around that moving fluid.
Those are not the 'reverse' of each other. So maybe the same blade design will not just get the same result in either case.
I'd be interested to see an expert answer.