Keep in mind that any practice is just a contrived situation and will seldom match any combination of events in a real life situation. At best, you'll learn not to cause your auto to jam due to ejecting into a barrier or finding your revolver cylinder won't rotate when held against a support. Any practice is better than none at all. Learning to handle the trigger and paying attention to where the working parts of your handgun are in relation to the cover is a definate plus.
I've always shot either handed and find my accuracy with my weak hand is about 66% of my strong hand but presentation and obtaining a sight picture takes about 50% longer until I've fired several rounds, after which it improves.