The new road probably would. For a while.
Trouble is, new roads tend to generate even more traffic.
It happens for several reasons. For one thing, if given an unimpeded strip of asphalt, drivers will find reasons to use it. They might make more trips simply because they think they can get around. Also, any new road is a magnet for growth. A beltway around Fredericksburg would open up more land for residential and commercial development.