There are several factors involved in this, and mouse polling is one of the least impactful.
First, games can use either "hitscan" or "projectile" hit registration, or a mix of both depending on the weapon. Some games like Overwatch also have beam (continuous damage) type weapons, which can also be programmed in different ways. Beams can have a lingering hitbox, which is intended to help the player with tracking, but is also means that a player can keep doing damage for a couple of milliseconds after they die. If both players are using projectile weapons, the travel time alone can be enough for both players to land a shot on each other. There is also the situation where one player, who has a projectile weapon, fires first, and the second player, who has a hitscan weapon, kills the first while the projectile is still traveling.
When two hitscan weapons are involved, it all depends on the game's netcode. Most games these days use a "shooter's advantage" hit registration model, which means that for example when you shoot an enemy that is moving to hide behind a corner, your hit will still register even if your enemy was already behind that corner on their own screen. In some games this also leads to the "lagger's advantage" where it's possible to shoot people who have moved a considerable distance from where they look to be on your screen because your ping is high.
The shooter's advantage has the knock-on effect that if both game clients send a "shoot and hit" event to the server at roughly the same time, it takes time for that event to reach the server (due to ping). So if you have 40ms ping and you shoot your enemy and kill them, it's still possible for them to fire a shot in those 40ms, regardless of their ping.
Input lag can play a role in the moment when the hit is registered on the client level and mouse polling is part of that, but the majority of input lag is a result of the signal from your mouse having to go through the CPU first and then the GPU as they are processing the frames. That is why most competitive gamers play at 144 or 240 fps.
All in all, there is no one definitive answer to this question as it depends on the game, the hardware and your internet connection.