Nope. Try unplugging a SATA or PATA drive while it's switched on - guaranteed bluescreen.
Bolleux Sir Booglebox .... Bolleux ....
(a) A "bluescreen" does not count as turining itself off in by books ! After my initial question, the OP clarified that the computer really does
TURN ITSELF OFF..... that sort of behavior is absolutley nothing to do with hard drives (or even hard drive controllers) and is a deeper, more sinister hardware problem.
(b) Maybe on Microsnot Windblows, but you won't get a bluescreen on Linux or Mac.
(c) What about hard drives in a RAID configuration.... no bluescreen, no crash... no damage to drives.... I can happily plug and unplug SATA drives all day whilst the system is live !