I bet it will have a pretty large impact. The top five streamlines in this image pass over the car pretty much unmolested. If you stick some large diameter tubing in their path, Cd will increase. I'd imagine that the impact would be smaller on streamlines that are going to pass through a radiator or under the car, though.
Cylinders have high drag. Ellipses have lower drag, and streamlined bodies have the lowest drag. But you're not really interested in fairing each of the tubes of your bully bar, relative to the wind as presented to each tube, right?