Not always, US Virgin Islands is the only part of the USA which drives on the left side of the road but most of their cars still have the steering wheel on the left.
That would be a very good idea. especially if you plan on driwing a motorized vehicle of mass destruction (such as an automobile) .
I live in a "drive on the right side of the road" country and visiting Britain and the US have showed me just how difficult it is to kick simple habits like "look to the left before you start crossing the road" and "look to the right before passing the center divide".
There are many such simple rules that we have been taught so thoroughly that we dont even know we are obeying them ;-))
But NOT by practicing driving on the wrong side of your native roads. the other motorists would learn more than you did. And they would be quite unanimous in hating you for 'teaching' them.
Check out the Auto Clubs in your area, they often have a course like you need.