No, the BB drop won't affect that by itself. BB drop brings the BB closer to the ground, with more drop.

Your saddle position is set based on a measurement from the pedal or BB, or just based on leg extension while pedaling. The height of the top tube relative to the BB does not matter much, except for standover clearance. Anything low enough to give you good standover clearance is not too high and hence acceptable. Exposed seat tube length is also varied based on frame size and top tube angle. These are not affected by BB drop, in any necessary way.

You could spec out a frame with level top-tube, minimum standover clearance (highest seat tube position) and vary the BB height. The seat tube would get longer for a lower BB, and the exposed seatpost would then get shorter. This would start to look like a French Fit or a 1930s French randonneuse. In this case as you lower the BB you might need to shorten the head tube to keep the handlebar from becoming too high.