My understanding from the video here and from what else I've seen (here on Reg in some BAE rant? :) is that the laser needs to maintain an amount of time on the same, or at least proximate, spot. The area at target is probably less than an inch, so I imagine that the accuracy of which you speak of at the turret's end could also apply to the drone, which has a lot more control over its immediate domain.
Once these lasers can burn a hole within a second or so, of course what I'm saying is moot - but these current systems aren't *that* powerful, no?