Have you ever tried to start a super old fridge or AC that you unplugged without waiting the full 3 minutes before plugging back in? It sounds like a diesel truck shutting off in your kitchen.
Modern fridges absolutely keep track of pressure and time.
No, I admit I've never powercycled a fridge nor ever seen a reason to.
Can you explain the mechanism by which a fridge unplugged then replugged a minute later sounds like a diesel truck? The compressor pumps aren't continuous duty, they spend most of the time powered off anyway.
edit: I did some web searching and the only mention of wait times before plugging in a fridge I can find is waiting a few hours before plugging in a fridge if it was stored on its side. Unless you're also flipping your fridge over when you power cycle it, I don't understand why there should be any problems.
I believe most fridges use bimetallic thermostats to control a relay to power the pump. And they don't sense pressure or keep track of time.