Sundie,
Well, close....Basically, the condenser provides a path for the voltage created by the collapsing primary field in order to complete the circuit and produce a current which is necessary to induce a voltage in the secondary. In fact, the combination of the coil and the condenser creates a series tuned circuit that "rings" at the resonate frequency created by the coil and condenser when the points open, so the resulting secondary voltage is a very brief AC excursion.
Without the condenser, the relatively high voltage created in the primary by the collapsing field (about 500 Volts) will jump the very small gap of the points as they open, but not the larger gap of the points when they are fully open, so the result is a very brief flow of current across the gap of the points as they open, which does induce a relatively low voltage in the secondary. As the engine speed increases, this initial very small gap is short lived, thus limiting the secondary voltage.
When the points close, they bounce. The initial contact will start the current from the battery flowing in the coil, but a few milliseconds later, the points bounce open and the small accumulated "charge" in the coil will collapse and produce about 300 volts across the points, which are almost closed, so the voltage is enough to jump the gap. Then the points close again, and bounce open again, so yet another small spark is created until finally the points stay closed and the coil can fully charge up.
Bouncing points also shorten the effective dwell angle. If the points are bouncing for, say, 5 degrees, then the dwell angle is effectively reduced from 93 degrees to 88 degrees. This phenomena is most acute at higher RPMs because there is less time to charge up the coil and a shortened dwell angle reduces the available time even further, resulting in high speed miss which cannot be curred by just cleaning the points.
When the points open, there is the initial creation of voltage in the primary by the collapsing field so something similar happens and there will be a small spark as this initial voltage jumps the gap of the almost closed points. Less bounce occurs with points opening of course, but there is some flexing of the stationary point that attempts to follow the moving point as it opens and it will "catch up" to it and reestablish contact, so there could be several sparks as the points open as well due to contact bounce, but not as severe as closing points.
Higher quality points are designed to minimize contact bounce. This is done with a stiffer spring and a more solid mounting for the stationary point and a reinforced arm for the moving point. The bounce in really poor quality points can be so bad that a spark in the spark plug is created when the points close due to extreme contact bounce. This means that a spark is created in a very advanced timing position, about 180 degrees before it is supposed to, like during the intake stroke.
Even the best points wear out in a variety of ways. The mounting for the stationary point weakens and starts to flex more, leading to more bounce when the points open. The spring weakens as well which leads to more bounce when the points close. This can be seen as more obvious sparks coming from the points.
So, take a look at spark of your points when they are new. If the sparks get worse, and cleaning the contacts does not help, the points are done for and need to be replaced. And don't buy cheap points.
A perfect set of points would open and close instantly and no spark would be created. That perfect set of points is called a transistor.