Yes, the monkey will be hit. Both fast and slow darts will do the trick.
Work Step by Step
As shown on page 186, the dart falls below the straight-line path by the same vertical distance it would if it were dropped from rest and fell for the same amount of time. However, the monkey falls in exactly that fashion, since it lets go when the dart is fired. They will meet in mid-air. A fast dart will meet the monkey sooner, at a higher height.