Just played a game where I was Akali and was in a fight with a Lee Sin who had Guardian Angel. I was one auto from death but I killed him and his GA activated, yet he still hit me and I was killed in a situation where I would have been completely fine.
His auto was still out. You don't tend to see it so much on melee champions (given that it's already rare on a ranged champion, and now it's even harder because melee autos have basically no travel time, since they're, you know, melee), but if your auto is in motion when you die, your auto will still connect.
