Being able to effectively use a firearm with your support hand can be very important, but it requires practice to be proficient.
While gunfight statistics show an unusually high ratio of wounds in the primary hand and arm, there are other reasons to be ready to use your support hand to shoot your defensive firearm. Injuries to the primary hand (especially slipping on ice and injuring wrists) can leave you with no alternative but to use your support hand. When this happens is not the time to figure out how to use this hand in operation of the firearm. The time is prior to the incident.
The support hand is not “dumb” when it comes to shooting, it is simply at the same point that your primary hand was when you started shooting. Teaching your support hand these skills is important, and should not be neglected. Having equipment to support support side carry is also important to have (and have broken in).
Remember that an ounce of prevention can be worth a pound of cure. Practice ahead of time.
Always be safe and remember the 4 gun safety rules!