Capacitors that are in the audio path (as opposed to the power supply filter capacitors) can definitely change the sound of a component as they age over time, especially if they have a DC voltage across them as in a blocking capacitor. The problem is that capacitors have not really been used in this way since the widespread use of integrated circuits rather than discrete transistors - in other words at least since the 1970s. Vacuum tube circuits use blocking capacitors which may have hundreds of volts DC across them, and these capacitors can certainly influence the sound. In discrete transistor circuits that use blocking capacitors the DC voltages are much lower, but the capacitors still will change their characteristics over time.

In my tube amplifiers I use this aging effect to in effect "tune" the sound character of the amplifier to match the characteristics of the speakers. The use of oil capacitors in the circuit path is widespread in tube amps as a way to achieve this.

I would certainly say that components manufactured in the 1950s and 60s changed their sound from the time they were new, apart from the aging of vacuum tubes. Whether this would qualify as "break-in" is a matter of perspective.