Wouldn’t the Roman Empire had need of these, and many other things, on a scale that would dwarf anything in Europe at that time?
However, digs at several long-term legionary forts in Germany and the UK have found the remnants of facilities for mass producing pila and ballista darts, and it would not be terribly surprising if they could also crank out large numbers of arrows for the auxilliaries.
Romans leans towards darts (closer to lawn darts than pub darts) and javelins for range weapons. Roman legions weren’t built around individual skill, they were built around a lot of people working together. Infantry men could throw darts and javelins until the enemy closed to hand distance and just drop what they hadn’t thrown on the ground. That way you didn’t have a big chunk of your force useless during different parts of the battle.