After thinking about it more, I realised you're absolutely right. It doesn't matter if the laser designator beam takes a knuckleball path through the intervening air; if the laser dot is on target---classical optics are time-reversible---the shooter will see it on target. The effect of those same air density variations on the bullet is similarly irrelevant [1], because the bullet continually aims for the laser dot.

It works by negative feedback, like a servo; all the error terms in the middle cancel out. Neat!

[1] The refraction of a laser by air density variations is bound to be different from the ballistic effects of those same density variations on a bullet passing through them. But it doesn't matter, because the corrections are applied continually along the trajectory, not at the source.