A radiator generates lift/drag when air passes through it for the same reason why any angled surface generates lift/drag when air passes over it. The only difference is the quantity of that lift/drag.
As stated earlier, it's possible to exploit those forces by changing the angle and/or shape of the radiator to gently nudge the car's center of pressure one way or the other. The rules are so tight, you almost have to look into such solutions.
That said, I do wonder about how much can actually be gained.
(Click each to enlarge)
I've always assumed - could be wrong - that teams try to direct turbulent flow into the radiator inlets due to the fact that turbulent convection is better than laminar convection. That would seem to enable a measure of flexibility in terms of inlet size, shape and placement. In the photos above you can see how teams have placed various aerodynamic devices upstream to the inlets.
The white appendages between the upper and lower wishbones on the BMW appear to have sent an eddy to the radiators. The camera housings on each car seem to have been placed with similar intentions, and I think it's also the reason behind both the Ferrari's brake duct winglets and the front pull rod.
How does such turbulent flow affect the lift/drag of the radiators it impacts, and would those benefits, if any, outweigh the benefits granted by the relative freedom to optimize the size and shape of radiators/sidepods for overall efficiency?