Role of a ball in a fountain pen's converter
I don't have that particular pen, so I can't view the ball you're referring to.  However, I suspect what it is.
Fountain pens work by capillary action; a minute amount of ink is allowed to flow to the nib.  If you tried to refill the pen at that rate, it would take forever (about the time it would take you to use up the ink in the pen by writing).  The converter contains some form of valve that opens when you suck ink into it, and seals when you're not refilling.
A ball is a common mechanism for a valve.  Something springy holds it against an opening so the opening is normally sealed.  Negative pressure inside during refilling pulls the ball away so ink can enter quickly.  However, other kinds of valve mechanisms can be used, or if there is a ball, it may just not be in a visible location in some converters.
If the ball in your converter is free to move around in the tank, then it likely serves a different function.  If you fill the pen with pigment-based ink, there might be a tendency for the ink components to settle or separate if the pen is stored full.  The ball could serve the same function as the mixing ball in a spray can.  Just changes in the pen's orientation when writing and putting the pen down or in a pocket would move the ball through the ink and keep the ink uniformly mixed.