Remember that the in your first example, the cable is only taking load when it's engaged, and in this case, that would be when it's in tension.
In a truss, the diagonals are designed so they are always engaged in either tension (if they are downward pointing "V" shape) or compression (if they are upward pointing "V"s). Therefore they are always transferring the applied load. Trusses are really good at handling axial loading, but don't do well in lateral loading so, if the loads are applied correctly (aka: at a panel point) then all of the parts of the truss will only either be in compression or tension, and not in bending. (There are zero members that actually don't really do anything so keep an eye out for those as well.)
If this truss only had the 10k load over joint E as shown, and none of the other adjacent forces, would that diagonal (E-K) be 0?
No, because if diagonals of the truss are always engaged, then the diagonal will always be taking some of the 10k.