No, it's not impossible, you don't need to alter the frame, and such conversions can work very well indeed - you get drop bar aerodynamics and MTB tyre choice and offroad traction.
Do a forum search for advice; this has been discussed here before. The key problem is getting drop bar shifters that are compatible with MTB derailers (btw, it would have been nice if you'd told people that your bike is an MTB rather than leaving them to google.) There are at least three solutions - a shimergo conversion, bar end shifters, and the minoura space bar hack using MTB gear shifters, if there are any break leverless ones compatible with your derailers. Shimergo is probably coolest, bar end shifters is the easiest.