Will Hordes from the city be a real thing?

In a SHTF where replacement Water/Food is unobtainable, (Power outage, Economic crash with store and banks closed). We hear time and time again that “Hoards of thousands will flee the city”. Unless it’s a nuclear war, many will not even realize that the SHTF for a day or two. Most people will probably be using supplies & water with little rationing, thinking that everything will be OK in a day or so. Especially if it’s something like a grid-down scenario, where many will just assume…