Probably. I'm not completely familiar with the Dew drop, but if it's like a standard drop bar you'll probably just have to get new brake levers. I would guess that your bike has v-brakes or discs, so you'll need to get either v-brake road levers (like tektro rl520 -- I have them and think they're great) or get travel agents because standard road levers don't pull enough cable for v-brakes or disc.
If your shifters are on the flat bar (which they probably are) things can get further complicated since most road bars are larger dia than a flat bar. Grip shifters can sometimes mount to the bottom of a drop bar...and I've even seen some people mount them onto the tops of a drop bar -- but it usually requires spreading them a lot...which I wouldn't recommend.
If you have a lot of experience with this, it's not too hard at all. If not it might not be worth your time. You might just look at adding bar ends to the flat bar to get some extra riding positions. A lot of people actually tour with flat bars out there, so you'll not be at any disadvantage.
I love drop bars, but also do just fine on a flat bar with bar ends. YMMV
