Yes all modern hard drives park themselves when power is removed automatically. Only very old MFM hard drives (circa the mid 80s) had to be parked by hand. That "thunk" you hear when a hard drive powers off is the head moving over to the edge of the platter... and parking itself. This is also why hard drives are rated for both "operating" and "non-operating" shock values.
Read/Write heads ride off the surface of a disk by margin of about 3 to 4 nanometers. It relies on a cushion of moving air (driven party by the motion of the spinning platter) to keep it from plowing into the magnetic surface of the disk with deleterious results.
If the computer is off, than the Hard disk's platters are not spinning, and the head is parked.
If the head were not parked, and the platters were not spinning, you'd have a real problem the next time the drive went into spin-up.
Yes all modern hard drives park themselves when power is removed automatically. This is also why hard drives are rated for both "operating" and "non-operating" shock values.