Nah. They need to push the gunpowder in from the "boom" side. We also count the "outs". Anchor into the cannon is a separate step and cannot just be hung on the outside.
Boom, gun powder in, stick out, anchor in, stick out.
5 strokes unless we count a "suck" for cooling the barrel.
Now that I think of it (far more than a silly topic actually deserves), I’m convinced it’s a 2-stroke mechanism. Loading and firing are separate stages of the normal operation cycle. Think of that like the two stages of a power cycle of a 2-stroke engine.
Piston moving up is like cannonball and gunpowder going into the barrel in the loading stage. Gasoline igniting and moving the piston down is like gunpowder burning and propelling the ball out of the barrel.
In a typical 4-stroke engine, there is a process for resetting the engine between power strokes. The energy for the other three strokes (exhaust, intake, compression) comes from inertia in some sort of flywheel.
The "power stroke" in this system is not the gunpowder. It is the winching in of the cable.
In this system, the cannon is analogous to the flywheel: It merely resets the system between power strokes.