To back up a bit, I think I would first experiment by holding down the on button while you are plugging in the drive and while removing it and see how it responds. I've tried similar things on some circuits that if you held down the button it wouldn't work as it was only looking for a short pulse.
If it works when holding down the button for a long period and while connecting and disconnecting the drive you could just hard wire it on all the time like you originally wanted to do.
To answer your question "can this functionaly be mimicked in electronics?", the answer is yes. You can mimick just about anything. I know you could use a 555 timer IC to make a circuit but someone else might have a simpler circuit. I'd have to do a little research to come up with a circuit for you. Someone else might have a good one ready to show you.