It depends on the box's boot sequence.
Thomson boxes will boot without a drive, but they seem to be the exception. Most other boxes require a drive, and it seems that the drive has to be a minimum of 200Gb so that the box can reserve 140Gb for basic functionality before it then goes on to see that there's no subscription.
Short answer then is "probably not"
It's a reasonable idea to salvage the drive, but only if it doesn't affect the box's operation; and in most cases it will so you'll end up with no satellite TV.