Not necessarily, though if you are rarely in the drops on your road bike you are not getting the aerodynamic advantages they provide, and that can be very significant if you want to go faster or to maintain your speed into a headwind. Bear in mind that the resistance of the air is the main constraint on your speed.

The same applies on a tourer. Obviously speed is less of an issue on a tour, and a loaded bike is going to be less aero anyway, but judicious use of the drops can save you some energy especially in windy conditions.

Having said that, touring bikes with drop bars are very much a British and American fashion. Most of the touring bikes designed in mainland Europe, for example, have flat bars. I've done both. At present I have a heavy-duty expedition tourer with flat bars. I sometimes ride over pretty rough terrain and when heavily loaded, wide flat bars help a little with stability under those conditions. On the other hand, for light touring on paved roads I tend to put a saddlebag on a road bike with drop bars. So it is very much influenced by your personal preference and the sort of touring and terrain you will encounter.