Honestly, this tends to hinge on two major factors: the cause of the damage and the age of the roof. If your roof is damaged as a result of wear and tear, they will not cover the damage. The same can be said about roofing that's damaged as a result of foolish behavior or actual intentional harm. Moreover, many companies will not cover roof damage on roofing that is over 15 to 20 years of age. Unless you can get a professional inspection that certifies that your roof is in good condition, getting coverage won't happen. As long as your roof was in good condition and was damaged by means outside of your control, you have a shot at getting coverage.
To max your chances out, make sure to get a plan that covers wind, hail, and ice, too!