In the 90's VW had a Passat with no grill in their range (this generation of cars was not available in SA). The air for the radiator went through the badge on the nose. I drove a diesel Passat Variant (station wagon) like this, who belonged to friends from Frankfurt, on the Autobahn in Germany. At 140km/h, you get overtaken by literally - EVERYONE!
In hindsight, I must say I think a lot of air is also scooped up by intakes underneath the bumper, which I suppose is the case with the BMW as well?