It will work, and maybe sooner than most people think. It has a very specific application: shooting down missiles launched nearby (this side of the horizon as viewed from an airplane) soon after they are launched. A missile at launch has a heat signature that can be seen for miles, and has no possible effective countermeasures like decoys that are available after ICBMS have deployed warheads.

It would be useless as a defensive weapon deployed on our coastlines, unless someone launched a short-range missile from a sub. I suppose it could be used to knock airplanes down, but I don't know how many shots one plane can carry (it is limited by the fuel for the lasers).

It would have been useless defending us from the Soviet Union, which like America, stored its nuclear missiles thousands of miles from the borders in the center of their continent, where no laser plane outside its airspace could shoot the missiles at launch.

It would be spectacularly useful in Iraq, where we control the airspace, and one or two planes could cover a huge portion of the small country. It would be useful in guarding North Korea, a small nation on a peninsula. I believe most potential missile launch sites would be in range of laser planes patrolling offshore.