Not necessarily; it might be possible to have some balls collide in such a way that at least one comes to a stop. At least one ball will keep moving though, and it isn't clear to me whether it is possible to prevent that moving ball from, eventually, hitting that stopped ball again. I think that would require at least three balls (ignoring pockets)
This is a problem of energy conservation: the cue ball starts with E = 1/2 mv^2 kinetic energy and, no matter what, that same amount of energy has to exist afterwards in some form.
But where will it go? In an elastic collision, a negligible amount of energy gets converted to heat (through inelastic deformation), and only a small amount will be converted to sound.
The only other place the energy can go is kinetic energy distributed between the balls. This means that there's no way to cause the balls to collide such that they're stationary afterwards.
Hypothetically, you might be able to completely convert the linear motion into rotational motion and have the balls spinning on the spot afterwards... but that's about it.
That's why I wrote "At least one ball will keep moving, though". I agree it might be possible to convert all kinetic energy into rotational energy, but that requires you to be able to get a ball spinning. I think that requires friction, which the OP I replied to ruled out.
I can't see how friction is factoring into the directions the balls initially scatter, as it's not taking the rotation of the balls into account. With that being said, wouldn't the balls all go in the same initial direction as they do in the linked example? Aka, the ones that are moving would move in that direction. Theoretically they could eventually bounce off walls and collide into each other in such a way that they eventually stop (though then there's the possibility of other balls that are still moving colliding into them later).
