Hybrid bike change to road bike
No, road brake levers are not compatible with v-brakes. If you're dead set on switching to drop bars on a bike with v-brakes, you'll need to either switch the brakes to cantilevers or use a travel agent to correct the pull ratio. Personally, I'd just switch to cantilevers. I've never used a travel agent, but I've heard they can be finicky.

There's also a question of shifting compatibility. The first thing to check is that the brands match. Sram and Shimano are not cross compatible, so if you have one on one bike and the other on the other, you'll have problems. 

The second thing to check is the number of gears. Ideally, you want the same number in the front and the rear. If they're different you'll have problems. 

You also need to know if the mountain components that are most likely on your hybrid are compatible with road shifters. If it's all 9-speed Shimano, you should be good. If it's 10-speed Shimano, you're going to run into compatibility problems. One more thing to mention with Shimano is that they have sometimes used hybrid specific front derailleurs that work with just fine with mountain shifters, but sub-optimally when mixed with road shifters. Sram 10-speed is all cross compatible between mountain and road. And I don't think Sram even makes 9-speed stuff anymore. If they do, I'm not sure whether or not it's cross compatible between mountain and road. Someone else, feel free to edit it in. 

I know, you practically need a flow chart to keep it all straight. If in doubt, check with your LBS.

It's also worth pointing out that your position on the bike will change. Road levers will put you leaning farther forward on the hybrid. It'll be enough to be noticeable and possibly uncomfortable. You might be able to correct with a different stem, seatpost, and/or seat position. But be aware if you start messing with the stem you're going to change the way the bike steers.