It seems the player will try to do the logging out animations, i.e. the f3 animation (sitting.) Then crouching again, but when it does, it seems the player stops holding onto the ladder and falls. It's not that bad of a bug, but players with bad internet could suffer the same fate I did. I hope it gets fixed.
-Thanks!
p.s. I did a controlled experiment by quickly turning off my router and turning it back on while at the top of a ladder, I tried it 4 times near the top, every time I lost connection I died. I have not tried logging out somewhere near the bottom of the ladder, maybe you guys could try it out?