I have a bit of a Frankenstein bike made from odd parts and it has straight handlebars with twist grip gears fitted to an old road bike style frame. I hate the straight bars but love the twist grip - is it possible to retain the twist grip but change the bars to drop down?
Most drop bars have a different diameter than flat bars, and therefore cannot fit a twist grip (which is designed for flat bars).
Moreover, you have to get the twist grip to an appropriate position on the bar so you can shift easily. Some BSO's have drop bars with twist grips, but these allegedly have been sawed in half to get the twist shifters on from the center and are being held together by the stem. This is not a good idea.
The easiest way to get twist shifters on a drop bar is a HubBub drop bar adapter, which plugs in as a bar end for the twist shifter to be attached to. Though, it will likely be easier and better to just switch to bar end shifters or some other type of shifter (stem shifters, downtube shifters, brifters, etc.) As DRH said in the comments, you may end up shifting accidentally when using the drops.