There have been fairly similar things happening before. Consider Edmonton during the 2010 US-Canada gold medal hockey game:
Here the green represents the previous day while the blue is the day of the game. Note the preparation before the game and the intermissions. The difference in the peak and trough at the end of the ceremony is 140 million liters. In a city of less than 900k people, this is about 160 liters per person. That's a couple dozen flushes each.
However, the biggest issue is that people aren't the only things that use water. According to this article, industrial water usage represents 40% of municipal water usage. So you would expect to see only an increase from 100% to 160% if someone did this.
Now, my city, Calgary, used 176 billion liters of water in 2014. This is over 20 liters per minute on average. Surely the peak times are much higher than this mean. The 1.2 million flushes of one gallon of water taking one minute to fill would only increase the mean by about 6%, and surely the peak is significantly less.
I think it's safe to say no, it would not come close to breaking.