Water supply systems would be just fine, because they are designed to support fire hydants. Fire hydrants are FAR more demanding than household water systems. The neighborhood flushing all at once would mean that your toilet tank would take a little while longer to refill than normal.
Sewer systems, however, may be overloaded. So if you're "downstream" enough from your neighbors, it is possible that the system could back up into your toilets, bathtubs, and sinks, especially the ones in the basement and ground level.
(actual civil engineer's opinion herein)