Generally speaking I'll agree but, you should be equally adept at shooting either pistol first. The advantage Double Duelists have over any other category is the vast array of transition options available to us. But you cut that number of options in half by only using your dominant hand first. If you're going to shoot Double Duelist you should practice drawing and shooting with both your dominant and weak hand first.
Let me give an example as to why. Stage calls for pistols to be shot at position 1 then move to position 2 to shoot shotgun. I shoot a SXS shotgun and load the shells with me left (weak) hand). On this stage I'll shoot my left pistol first. When I'm done with that I holster it then draw and fire my right pistol. As I'm firing my right pistol I'm pulling two shotgun shells with my left hand. When I'm done with my second pistol I holster it as I'm taking my first step toward position 2. As I'm moving to position 2 I have the shotgun shells up at eye level with my left hand and my right hand is reaching for my shotgun. (Reaching as you move helps you move faster. ) When I get to position 2 I grab and raise the shotgun to my shoulder as fast as possible where my shells are already waiting to be dropped into the chambers.