I think what he's asking is whether you could use the torque implied by the rotation of a bolt or bolt head moving after the cartridge has fired and the energy imparted into it has already forced it to move.
I can see where he's going with this. He's asking if one could run some variety of rotary cannon using the power generated by the recoil to spin the entire mechanism, using the mechanical energy provided by the implied torque generated by a locking lug setup.
While the torque implied by each barrel or bolt head is negligible, an accumulation of torque might be enough to actually rotate a collection of barrels around a center spindle point. Observe the diagram I threw together very haphazardly and in a mere few moments:
A. According to Newton's First, and Third Laws of Motion, the force being exerted backward against the barrel is equal to the force of the lead being expelled from the barrel. That equates to a backwards pressure which acts against B.
B. A set of locking lugs set into a helical channel of some variety. These locking lugs force the barrel to twist as it recoils, imparting a small amount of torque into whatever armature that is suspending the barrel mechanism.
C. As each barrel is fired, it twists on its own, imparting a small amount of torque to the main spindle.
D. Cumulitive torque moves a spindle composed of individually-spinning barrels. If the spindle spins, and mechanical doodaddery behind the spindle loads and fires each individual chamber, what you'd have is a device that would spin faster and faster just so long as ammunition is fed to it,
I can see where he's going and if my explanation follows the original poster's description, I can explain exactly WHY it wouldn't work.
1. a freely-spinning barrel wouldn't work, mechanically. There would be no channels for the lugs to react against, therefore the individual barrels would recoil straight backwards, rather than rotating. So, for there to be any rotation in the system, the barrels would have to ride in channels representing a helix shape.
2. If said barrels were loaded into a helical-shaped channel and reciprocated within this channel, they would require springs or some other variety of piston to push the barrels back forward, running them in reverse against the direction they just so recently recoiled. This leads to a negative expression of torque. +1 - -1 = 0. Unfortunately, by adding springs, you've negated any torque that you would have created.
Therefore, based on my understanding of the OP's query, a torque-powered gatling system cannot work.
But! There is good news! If one were to replace the locking lugs with a ratchet mechanism, one could easily capture the mechanical energy inherent in a reciprocating bolt, transfer that to rotational force via a clever set of ratcheting planetary gears and therefore utilize the force of the expelled lead to spin a gatling system, rather than relying on an outside force or gas system to keep it running.
Keep in mind, the above paragraph was wholly educated speculation and is quite possibly not feasable. Your Mileage May Vary.