Not only is it possible, but it is a great tactic when prospecting a new stream to figure out what's working.
You definitely have to modify your cast to keep the loops larger and more open, similar to the way you would with a sinking line. I find it helps to slow everything down to make this work well, for example focus on making sure your line is extended fully at the end of each cast before executing the next one. Adding a slight downward movement of the elbow on the forward cast (and upward lift on the back cast) can help open up the loop.
If I imagine it in my head, I think that when you cast just a dry fly you keep the loop tight and straight, the line extends fully and then falls onto the water. In the case of a dry/dropper rig, I imagine the line rolling out onto the water because of the bigger loop.