No.
Because when the ECU (at least, on six of my cars) detects the misfire, it no longer pulses the injector for that cylinder.
The car will run poorly, but it won’t damage the cat, or engine, because there will not be any unburned fuel to wash down the cylinder walls or load up the cat.
I wouldn't count on that. When that CEL is blinking like a christmas tree, you'd best pull over and call a tow truck.