Only when he's playing dressup.

There's ways you can throw your right out without it becoming a sucker punch. For one you if your opponent reacts to your shoulder feints you can feint a jab and come back with a hard right. You can also draw him in by provoking a counter that you can see coming, or forcing him to throw the punch that you want him to. Practice drawing and slipping while you are sparring. If you can find an opponents bad tendency and open it up further then you nail him with any of best punches.

A lot of fighters drop their left when they think you can't reach them. One neat move that Rocky Marciano used to great effect is his "phantom overhand." You make them think you are going low by moving your eyes from their eyes to thier body. You do this as soon as you take a step forward. . You drop your knees and perhaps a hand if your opponent needs more convincing. Then you spring up violently put his head in your sights and throw the best overhand right that you can.

If done quickly it'll be too late for him to keep it from coming. You twist your right hand horizontally and you'll be able to get more distance by raising your rear foot forward.

Some other moves that take more explanation is the drop-shift which you move your left foot back and switch to lefty stance to set up your hooks or uppercuts. And various counters, greysnotsoold in his section gives you textbook knowledge on the matter.

As for pivot/no-pivot it depends what works for you. You can step forward, you can pivot, you shift/side-step. I think it's better to have good foot position to prevent ankle injuries and to give balance, as for a strong right I like to think of my rear leg to act as a hinge, or as a spring for a jolting punch a la Jack Dempsey.