I think that there would have to be alot to prove there - first, that you were overloaded, second that it was the cause of a failure, and third, that failure caused the accident. Put another way - if you were speeding and something happened and you crashed - was the resulting damage because you were overloaded, or because you were speeding.
Also, your insurance covers you even if you are intentionally negligent. They can't just not pay your victims just because you were in violation. So if you go rob a liquor store and are speeding away and crash into someone, your car insurance still must pay for the people you crashed into. They may not pay for your car though
One thing missing from this discussion though, is tires. I'm alot more leary of overloading tires. You are probably much more likely to break your tires before you break anything on your truck.