No. I would say, in fact, that the average American doesn't even know the term "Boxing Day", and that if you asked them, they would guess that it has some connection with бокс as a sport!
But although only Christmas Day itself on 25 December is an official holiday, in some years (as I said above), either the 24th or 26th may be considered a holiday by the federal government in order to give people a long weekend. This year, for example, 25 Dec is on a Sunday, and so Monday the 26th will be a holiday, making it a three-day weekend.
In years when the 25th is on Wednesday, it kinda sucks -- the government (and many businesses) may declare the 24th a "half day" and send workers home at lunchtime. But on the 26th, it's back to work! However, this is compensated by the fact that in other years, when the 25th falls on Tuesday or Thursday, it's customary to have a four-day weekend.