No this is not true. The magnetic field of the coil collapses when the points open, inducing voltage/ current which CHARGES the cap, which is an effective "dead short" at the moment the points open.
When the cap reaches it's peak of charge, it DISCHARGES into the coil, causing the coil to again absorb some amount of energy. This IS IN FACT WHAT YOU SEE with the tapering oscillations in the waveform. If you REMOVE the cap, there will be FEW if only maybe one or two oscillations, as the coil discharges into a very tiny capacitance,.........which would be the capacitance between the turns of the coil and other "stray circuit" capacitance caused by wiring, etc.