Can I add coverage after I've had an accident?

Unfortunately you cannot add collision coverage after an accident and then use that coverage for the accident; your coverage only becomes applicable for accidents that occur after you add the coverage - not before. The date of the accident is what they look at, not when you file the claim. At this point, your best course of action to is repair the damages out-of-pocket and add collision and comprehensive(sometimes called full coverage) for the future.