Yes they will. If the replacement HDD is identical to the original, it'll work fine.. as long as it's cabled correctly.
I've performed this many times.. using GHOST to create a copy of the original HDD to a new HDD.. then disconnecting the old (original) HDD, connecting up the new HDD..
Obviously minor problems may arise. Make sure the replacement HDD is jumpered correctly. It MUST have the same software on it as the original also.
As mentioned above, GHOST is the application I used to make a copy of the HDD.. which runs off a bootable MSDOS diskette. Alternatively, I'm fairly certain that most new motherboards come IDE controllers that support IDE RAID. That can create a copy of your current HDD.. without any software. But I haven't played with it.
Good luck!
Lachlan
Note: be aware, simply doing a Windows copy of all data on your original HDD to a new HDD will NOT work.