My 15 year old is a natural righty first baseman who couldn't throw in the fall due to an arm injury. He played some JV games at 1B lefty. He learned to throw well enough that you couldn't tell he was a natural righty when throwing back to the pitcher, or throwing ground balls to the infielders.
But live game situations was a little different. You become accustomed to doing things without thinking and switching arms requires thinking about things you're used to just reacting to. Arm strength is clearly different too and just takes time to develop...many months of long toss. I am certain it can be done at some positions (1B, 3B, 2B), less at others (SS, C, P). The key is do you have a feel for it in your finger tips. If you can throw the ball where you want, you can develop the strength. If you can't control the ball, it's an uphill battle. To do it, you have to change your life to the other hand and just do everything with the weak hand...eat, brush your teeth, drink, open doors, etc.