Not a daft idea at all. Mountain bike + drop handlebars = one cool bike, in my opinion.
As for the stem, 1 1/8 inch is standard for both road and mountain steerer tubes these days. But the handlebar clamp is a different size for drops than for a flat bar. You'll want a road bike stem that fits the drop bars you want - 26.0 or 31.8, for example.
Think about where you want the handlebars to be before you buy the stem -- I've found that a short, hi-rise stem works best, but it really depends upon the geometry of your bike and the position you like to be in when you ride. Get whatever width you are comfortable with. Some people get wider bars for riding off road, but I don't think it's necessary.
If you have an old mountain bike with a threaded headset and quill stem, check out
www.rivbike.com for a stem called the "dirt drop stem". Or, you could get a threadless stem and an adaptor.
For brake levers and shifters, I like to use regular (non-integrated) brake levers and bar-end shifters. It's cheaper than buying sti integrated levers, and you can switch the bar-ends to friction if the indexing doesn't work out just right. Cane Creek just came out with a nice set of non-integrated road brake levers that are shaped like Campy Ergo's.
www.harriscyclery.com has all this stuff.
Another thing you might need to do is, if you have v-brakes, get a "rollamijig", which is a little pulley that sits on top of the brakes and decreases the amount of cable pulled by the brake lever. Either that or it increases it, I can't remember - but if your brakes are impossible to adjust with the road levers, the rollamajig solves the problem.
Good luck!