You can't twist out a countersunk screw head or a rounded screw head. The best option is the electric drill with a screw bit and in reverse.
If it's stripped, then it should be just spinning freely in the slot and can be removed by tilting the casing sideways. Stripped means the screw thread is no longer available to grip the casing. So there shouldn't be a problem removing it. Unless what you mean is that the screw is very firmly stuck on the casing and you can't remove it cos it won't turn?
what I'm saying is the HDD usually is attahed to a tray'the tray and HDD is screwed together,I might be wrong for the recent popular non-removable battery kind
it could be just slotted directly to MB to save space.
and as what I know in computers manufacturer rarely use countersunk screws
if it is button head then great,it is safer to dremel out a new slot for screwdriver than reversing drill it