I tried playing with the order of the IK/path constraints and the only difference I found is if the path constraint is at the top of the list it does nothing whatsoever. Is that video trying to show how if you have two conflicting constraints the one higher on the list gets nullified?
My problem isn't that nothing is happening, the hand rotates and moves in accordance with the weapon's movements but the rest of the arm just stays in place.
Is the hand supposed to be using an IK constraint too? Right now the IK is just for the upper and lower arm and the hand is just a normal bone parented to the lower arm.
Ah! Figured it out! It just about placing the IK target within the weapon bone, that way the weapon drags the arm along with it!
Thanks for the help!