You can over draw the temper but annealed is pretty much annealed. With the tang that short I think that I would be more comfortable with getting a carbide bit and not change the temper. Jantz carries carbide bits. Carbide Connection, Congress Tools, and MSC Direct are other sources. Use a spade bit and keep the speed of your drill low. My feeling is that the tang was hardened and tempered along with the blade. With that short of a tang you will probably need all the strength you can get rather than toughness that comes with a softer steel. In short, the heat treatment given to the tang was meant to work with the short length.
Doug