Yes, you can train youself to shoot with your left hand.  It will take time and ammo, but it can be done.  You'll also have to reprogram yourself to use your left eye when shooting left handed -- unless you have a "dominant" eye problem.  See that discussion and what to do about it.

 

In order to master an activity, it will take a minimum of 2,500 repetitions of that activity before it becomes a habit.  You won't master left handed shooting overnight.

Exactly right. 

 

New courses being taught to our warfighters in Afghistan and Iraq include shooting from the "weak side" -- usually the left side for 4/5 of shooters and the right side for 1/5 of shooters.   There is also much practice at shooting from unorthodox positions at targets.  In an urban warfare scenario, you cannot pick the best position and you often have to adopt peculiar stances and shooting styles to engage bad guys.  New training procedures emphasize these relearned lessons. 

 

Police officers routinely have to qualify with both their strong hands and weak hands with their sidearms.  The logic here is that your strong arm may be injured, but you still have to be able to shoot and hit with the opposite uninjured hand.  There's a lot of wisdom in both these situations to take to heart.