There are drop bars that fit MTB clamps, but they tend to be different from road drops. The ones I'm aware of (such as the On-One Midge sitting in my parts cabinet) are designed for off-roading, so they are very wide, with extremely shallow, heavily flared drops. This makes the drops extremely comfy, and gives you great control, but doesn't give you a particularly aerodynamic position. I also found the hoods position to be rather useless (it was too flared to be comfortable, and not that different from the drops in any case), but others seem to disagree on that.

You'll still need to change the stem (drops add a noticeable amount of reach), and most likely need to replace the controls (the Midge is meant for road brake levers and bar-end shifters), so converting to them is going to be as difficult as converting to normal drop bars.

Alternately, there are some drop-shaped bar-ends you could try. I have no experience with them.