Did it to a couple of bikes for my wife and daughter. No problems. I can't think of why you'd notice much difference in handling--your hands will be in about the same place asif you were riding on the brake hoods with drops.
You could get much the same effect more cheaply by raising the drop bars to about the level of the saddle. In the quill stem days it would have taken 10 seconds, but now you'll need a stem. And you don't need new brakes, just new levers. In fact, there are bars around that will let you use road components. Check Rivendell and Velo Orange.