You might delay the electronic component a bit, yes. But it won't need to be as much as 200ms. A mechanical ('tracker action') organ actually has less delay than you might imagine.
The disadvantage to this classic type of mechanism is that the keys can be heavy, and everything needs to be quite close to the console.
150 years ago pneumatic action was popular. It enabled larger instruments, and suited the Victorian taste for the bombastic. A disadvantage was sluggish response.
Today, tracker action is back in fashion, with electro-mechanical action where distance makes it necessary. Delay IS an issue, but it's acoustic rather than mechanical. Organs tend to inhabit large buildings, sections of a large organ may be mounted some distance from the console for dramatic or architectural effect. sound takes time to travel, and what the organist hears may be more reverberant than direct sound.
Maybe organists should be provided with nearfield monitors, fed from microphones close to each rank of pipes! In practice they just hit the keys in time and manage to isolate their brains from the acoustic feedback!
Organ is not the only instrument where the player has to (often automatically and subconsciously) 'play early'. But not many have to deal with the delay from a unit at the other end of a sizeable church AND the earlier sound from more local pipes!
How does a pipe organist deal with latency or delay?