<p>When filament is too short for the extruder to push will there be a stop in printing on the Ender 3, meaning that I should replace the filament when the end of the filament is near the extruder?</p>

The extruder can't push anymore when the filament is past the extruder gear. If your filament has run out to that point, the print will
not
halt but print without a filament, meaning that the print will fail. You need to pause the print in time and then put fresh filament into the printer.
If the end of the filament is cut flat at the end and the new one is flat too, the new filament can push the old one out to the nozzle, reducing the waste to a minimum, if you can live without retraction for the amount of length that has to be used up. You could friction weld the two parts together to alleviate this.