Yes, but a really good egg timing PLC setup will ask you how you want the egg cooked (soft or hard boiled, though the health department frowns own the soft boiled now). It may ask you the altitude above sea level to vary the time because of the different temperature of the boiling water. Better yet, there should be a altitude barometer attached through an analog input card to automatically determine this correction. You know how those pesky highs and lows can dramatically affect your eggs. Maybe the egg could be held above the water until a thermometer, again input through the analog card, says the water is to the boiling point then actuate an output dropping the egg in, ever so gently. Perhaps the display could then should show a graphic of the egg with a type of bargraph rising as the egg gets closer to being done. Then the PLC should ring an output attached to an alarm. The screen should also warn the person cooking to beware of the hot steam. Perhaps, though, an output through some sort of mechanism could tip the pot to drain. Then there's the possibility of mechanisms to gently crack the egg. We won't let the PLC eat the egg. We can't let it have all the fun. Lots of opportunity for creativity.
I know it sounds like something Carakatous Potts would make in Chitty Chitty Bang Bang. Ian Fleming has nothing on me.