Probably not, since modern air defenses are effective against small missiles and even mortar rounds. Here's a CIWS in Afghanistan shooting down incoming mortar rounds.[1] (Read the comments for more explanation from people who have been there.) The CIWS has radar which can track not just the target, but its own bullets. It makes quick adjustments until bullets and target are in the same place at the same time.
On one occasion, a US ally shot down a hobbyist-sized drone with a Patriot missile. Very expensive, but it hit the target.