http://www.nhtsa.dot.gov/cars/rules/...ndex.html#P581
Part 581 of the NHTSA/ US
DOT
It's a safety requirement so you don't easily die from a low speed impact, like say hitting a wall at 10 mph.
For sure, if inspected, it'll fail. A police officer may issue you a repair order so it gets repaired. If not repaired within 15 days or 30 days (whichever, whatever may be), the tags can be suspended.
Just half-ass install the bumper to avoid being pulled over. However, expect your fender bender, if you're in one, to be very bad until your repairs are done.