That's not a sophisticated screwdriver. But it probably has a very high gear ratio to allow it to work with 6v and low current to give it a reasonable run-time. And there is no chuck to tighten that might justify the expense of a clutch.
If you can turn the gearbox from the screwdriver end when there is no motor connected and with a gentle (finger tip) load on the motor end then there is no clutch mechanism.
Also, feel how much effort it takes to turn the motor shaft with your fingers and imagine that multipled a couple of hundred times. And remember that the friction within the gearbox increases as the movement is multiplied when driven from the screwdriver end.
...R