Smart phones are great to have, especially when you are involved in a car accident. Snapping pictures and maybe having a video too, is great for proof for the insurance adjuster. Anytime you can add documentation to a claim, it helps speed up the process.
Some insurance companies really want to get the claim handled quickly and be on to the next one. They don't really want to drag out the claim and have it sitting on their desk. Using the smart phone you have will go a long way to help settle the claim quickly!