Here is a post from YuGiOhRealms that kind of ties into this. It is courtesy of phiefer3:
there's this thing often called the "game state" which is the state that the game is in. the game state includes whats in your hand, lifepoints, current turn, current phase, whats in play, whats face down, as well as certain other effects that happen at certain times.
the game state is checked/updated at certain times to keep track of whats goin on. the times when it is checked include: between turns, between phases, between atks, between chains, between steps of chains, etc. basically after anything that may effect the game state (note it is checked between chain links, but not during them).
one of the things that the game state checks for is for 1 or both players lifepoints to equal 0, this is why you can loose between links, in the middle of a chain. it also checks for cards like swords of revealing light to see if it will remain on the field (it also checks for those invisable "lingering" effects to see whether or not they are in effect), it also checks for the presence of an exodia victory.
this means:
oponents end phase/turn ends > game state is checked
your draw phase/turn starts > game state is checked
you draw the 5th piece of exodia > game state is checked, and you automatically win.
your opponent technically never even gets the chance to activate drop off (especially since even without exodia, after you draw, you have priority to respond to your draw before your opponent)