Right, the drop in the sense that as you rise higher on a globe, the horizon should start dropping below eye level. It has been repeatedly demonstrated that this SHOULD happen on a globe, in various simulators done by physicists and engineers ... who do not believe that the earth is flat (or never really considered it). This horizon drop has never been seen in the increasingly-numerous videos from amateur weather balloons and rockets.
Here's one of these simulators:
So when Neil deGrasse Tyson made those infamous comments about how at 120,000 feet there should be no visible curvature, that was actually damage control, because 120,000 feet is about as high as amateur weather balloons have been going, and they clearly show a flat horizon, without any sign of curvature. Except that, as per the simulators above, Tyson was actually LYING. No, it wouldn't look like the curvature we saw with the wide-angle fisheye lens on the Red Bull jump, but it would not be completely flat as Tyson claimed. Take the simulator above to about 120,000 feet.