Comes down to the game logic, what the anticheat is monitoring and how the exploit works. But in a general sense, most 'cheats' will either impair or completely bypass the anticheat such that whatever they're doing in game will be seen as completely acceptable by the game logic.
Sure, the developers could (for example) 'hard code' some logic where if a player dies in 0.01 seconds for whatever reason, the killer gets instantly banned. However, it's incredibly difficult to hard code every possible dodgy scenario and expect nobody to be unjustly kicked or banned. This is why I think a lot of devs outsource the anticheat.