I was trying to figure out if this would work on my bike a few weeks ago. I decided against it. I think this is a pretty good description of some of the problems you may encounter:
If you compare top tube lengths,
mountain bikes are longer at every
size than road bikes. The reason for
that is that drop bars put the brake
hoods, which are the principal hand
position for most road riders, a lot
further forward of the steer tube than
the grips on a mountain bike.
Obviously it can be done, and
depending on how your built and how
the bike is sized you may even prefer
it.
If you like the fit of the bike now
and you're not using a super-long
stem, you'll probably be pretty
unhappy with a drop bar conversion.
Source.
I think that the better solution is to add some bar ends to your bike to give your self some more hand positions. Here is the solution that I came up with while researching although I have not implemented it yet.
First I would add some bar ends regular bar ends on the end of your handle bars. Bar ends are very similar to to the hoods on a mountain bike. It is more comfortable for your wrists to be in an up and down position (although you will have less turning power).

Next I would buy these "drop bar ends". It took me weeks to find somewhere that sold them. I have not bought them yet but they look sweet. The key when installing them is to install them inside your your breaks and shifters. This will give you a narrow profile similar to what you would experience on a road bike. (If there is space you can also mount your bar ends inside too).

One problem left. You usually use the drops when you are descending and trying to be as aerodynamic as possible therefore you will be going fast. You will need a break on the drops to stay safe. Probably you don't want to move your brakes to the drops since you will probably be using the flats for more technical riding.
So you need Auxiliary ("Cross", "Interrupter") Levers. To quote Sheldon Brow:
Initially marketed primarily for
cyclocross, these are also an
excellent choice for the touring or
long distance cyclist, permitting you
to brake from the top part of the
handlebar.
Unlike the 1970s extension levers,
these don't interfere with the main
brake levers. They install in the
middle of the cable run.
I think that the best course of action is to mount one of these onto each drop bar. That way you will still be able to control breaking while on the drops.

This is not how you would be using the brake however this is the only picture I could find of it.
This is what your handle bars look like right now:
grip breakLever shifter bar bar bar bar bar StemAttachment bar bar bar bar bar breakLever grip
This is what they will look like after you have added the bar ends and drop bar ends:
barEnds grip breakLever shifter drops bar bar bar bar bar StemAttachment bar bar bar bar bar drops breakLever grip barEnds