AWOL:
By the time the micro sees the pulse and runs the code that says "I saw it", the bullet will be 100 yards downrange.
I think this is exaggeration.
A busy-polling loop even on an Arduino should detect the passage of the projectile before it has travelled it's own length, given a fast enough detector.
Besides, it may not matter about latency, as long as the latency is consistent.
The experiment I did years ago... the distance between the rifle muzzle and the point where we wanted the laser to fire was 12 inches. At Mach 3 (the muzzle velocity of the .222 cartridge we were using), the bullet travels that distance in about 300 microseconds. How many Arduino instructions can you execute in that time frame (remember every Arduino instruction is a layer of C code underneath). Maybe the code in pure ASM would work, but not C.
Conversely, a 4538 dual timer has microsecond "resolution" and has only nanoseconds of propagation delay between triggering and timing. And it's simpler and costs less. Adjusting the time delay is a simple matter of turning a potentiometer.
Simple is always better.