No - the minors do tile work, not the minims. In effect minors are the equivalent of the workers from current levels.
Minims never leave the nest and are not directly controllable; they take leaves from the drop-off chambers to the brood chambers where they become fungus & take waste to the refuse chamber. You'll get a free minim with every minor / media / major tile.
Mediae are probably the most efficient leaf collectors for cost vs. effectiveness. Minors can carry leaves, but suffer a slow de-buff when they do. Majors can also carry leaves but their abilities make them better used as fighters.