Jack, the condenser is just a simple capacitor. It is supposed to tame down spikes from contacts OPENING. In a generator, when the commutator segments leave the brushes, they still want to flow power, so the brushes naturally arc.
We usually put condensers at contacts. Points are contacts, mechanical voltage regulators have contacts, and some vintage gas tank sensors have contacts (like my '55 Customline). Expect to see a condenser at each location.
Your car is alive with spikes going everywhere. The battery tames most of that down, but a condenser (at the source) helps smooth the power, tremendously.
The condenser doesn't rectify, and it isn't directional. It absorbs voltage spikes, then gives the energy back when the spike returns to normal. This helps prolong contact life. If you are missing a condenser, I guess it isn't a biggie. Most folks only notice a change when the points condenser fails. If the points condenser opens, the points arc, causing a delayed opening, and premature points failure. If the condenser shorts, no spark at all (and the ballast resistor gets real hot.