Sure you can. Lots of folks have. I met quite a few going coast to coast on road bikes. The things you need to work out are:
- Gearing - Road bikes typically have gearing that is way less than optimal for loaded touring especially in the mountains.
- Durability - This can be a problem for wheels mostly. The rear wheel in particular. The solution is either a stronger rear wheel, a very light load, or a trailer.
- Geometry - This may or may not be a problem. Personally I kind of like a responsive bike.
- Riding position - Some find this to be problematic. I actually find aggressive road bike posture more comfortable. it keeps the weight off of the butt. You do need to have a form developed that lets the legs carry most of your weight and therefore doesn't put a lot of weight on the hands. This requires some core strength and not everyone can pull it off.
- Heel clearance - The shorter chain stays of a road bike make for a lack of heel clearance. Small panniers help. A trailer is another answer. Going really light and using a large seat bag in lieu of panniers is another answer.
My recommendation is to shoot for 20 pounds of gear weight including panniers and set a limit of 30 pounds max unless camping in really cold weather. This does not include water or food which are typically picked up daily or how ever often is possible. I think that goes better with the idea of touring with a road bike and makes for a comfortable ride. But that is just my opinion, some people like to carry much more.