Whilst you can do whatever you like with your bars, drop bars are designed to provide the rider with a lot of hand positions and freedom of movement between those positions. In my opinion a grip shifter will seriiously get in the way of this.
Most importantly, the grip shifters at the end of the drop will prevent you quickly moving your hand up the drop to use the brake.
Drop bars are at theier most usable (and safest) when they are uncluttered, which is why all roadies have shifters mounted away from the bars or integral with the brake levers.