I haven't heard of it being called series feedback, but you could well be right. I just call it "emitter degeneration", but that's only a specific case of "series feedback".
No, I'm talking about accuracy of the output waveform. The base is driven from the input source, which is a voltage signal, but the base current is not linearly proportional to the base voltage, as you know. The collector current is proportional to the base current, and the collector voltage (the output of the stage) is proportional to the collector current, because the collector current is converted to a voltage by the collector load resistor.
So there is an inherent nonlinearity between the input and output voltages, because the base is current-driven (at least from the point of view of how the collector current is determined; I don't want to get into another discussion here about whether a transistor is actually voltage-driven or not - not the least because I don't actually know!)
Two ways of reducing this nonlinearity are to add a resistor in series with the input (which converts the input voltage into a current, roughly), or to add an emitter degeneration resistor. In either case the voltage gain of the stage is reduced, and the distortion is improved. The emitter degeneration resistor is preferred, because it actually implements negative feedback and it also helps stabilise the DC conditions.
Sometimes you will see two emitter degeneration resistors in series, with a capacitor across one of them. In this case, the un-bypassed one determines the AC negative feedback and improves the distortion, and the bypassed one provides negative feedback at DC only, to improve the circuit stability.