We had to do some math with this one as we only had an office to test with.
We used a 6' Shooter with a 6' Target at 100 feet, and mounted the gun to a camera tripod and used a laser pointer to aim at the target. We put the laser in the barrel and then set the tripod.
We shot the gun 10 times with an average bullet drop of 1 foot. Because a bullets flight path is parabolic, we can then deduce the distance the dart would go before hitting the ground. At 50' the bullet would have dropped 4 inches, and at 100' it would drop an extra 8 inches, At 150' the dart should drop an extra 2 feet. And at 200' it would drop an extra 4 feet, then hit the ground.
We found the secret to the power of this gun is rear loading it. You have to have as little dead space behind the bullet as possible. And the trigger must be pulled fast to release all the power at once.
Let me know if my math is wrong here.
I believe your math is perfectly right. But you have forgotten several important factors here. The drop can change depending
upon humidity and temperature, wind might throw your dart off target, or many other things could change your range. My advice? Go outside, get a tape measure and test it. Even if it does get 200', TantumBull is right, and you won't be able to use it accurately.