I don't know, as I will not have it in hand until next week. That said, if I had to guess I would say no. But I expect it would be close either way.
The way I see it there there are a three reasons not to do that:
1. It's no extra work to screw in the entire unit versus just the black part
2. If you're in an accident, or even just a little bump, the rod would likely poke through the bumper cover causing much more damage than what otherwise be incurred
3. Weight savings
Honestly, why would you want to leave the rod in full time? What is the benefit?