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?
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.
When the end of the filament is beyond the reach of the hobbed stepper gear, your print will stop extruding. Some printers (i.e. Prusa i3, Craftbot 3, etc) have runout sensors. These sensors can be a switch or some form of a circuit that is broken when the filament isn't there to close it (I'm no mechatronics engineer or anything, so my terminology may be a bit off). When these switches are tripped, the printer automatically pauses the print, allowing you to come and rescue it. Fancier printers like the Craftbot 3 will actually send you an email when your filament runs out or even jams! Of course, that machine is over $3600CAD, and well out of most peoples price range. The Ender 3, being around 300 dollars, is not equipped with a runout sensor. Switches and 3D printing files to make your own are either cheap or free.
And yes, some filament may need to be wasted if you do a swap. Direct drive extruders have the same problem but at a much smaller scale. If you just feed new filament into your machine, you will lose all retraction (which is annoying) until the second length of filament is in. At the point where the filament switches, (depending on your extruder and print speed) you may get a small patch of under extrusion. Nothing that will seriously compromise part strength, but it won't be super pretty.
Hope that helps!