And if anyone has the old GM Frigidaires, DON'T use one in there, Mom made the mistake of putting her Downy ball in the machine, while it didnt damage the agitator, the up and down motion of the agitator pushed the plunger in on the ball and she had softener in the wash water, the clothes had to be treated and washed to get the residue out caused by the mixing of the Downy and the detergent.
I agree with Tim. If your roto-swirl were to break, someone in the club could probably supply a replacement, but why go through that?
I have seen a couple of in-service breaks on bakelite agitators, including a 1963 Kenmore 600 that had an entire fin break snap clean off it's straight vane (something to do with tennis shoes).
Better safe than sorry if you're worried that the ball is going to break something!
My mother gave me one of these many years ago when they first came out. I'm not sure if it was in the wash cycle or spin cycle, but it tore one of my shirts in the back. I hated the thing!