The limbs on all modern compounds are matched for weight. I doubt the extra limb will be a match for either of the other two. If they aren't matched, one could eventually make the cam(s) 'roll over' at a different time than the other, causing the bow to need to be 'tuned', or corrected. You'd find your shots would eventually hit either lower and lower, or higher and higher, depending on which limb is stronger.

The catapult idea's a good one.