When implementing an audio amplification circuit using transistors such as the common BC337, the base of the junction is biased using a DC voltage. This ensures that the transistor operates exclusively within its linear region and does not enter cutoff or saturation. Under these circumstances, there exists a linear relationship between the input voltage and output voltage, which is ideal when the objective is to produce a sinusoidal output. We would typically make use of a PNP and NPN pair in push-pull configuration rather than a singular transistor but that isn't particularly important, here.
The rise and fall times most commonly specified pertain to the 10% to 90% transition and so within the context of amplification, these values are fully applicable.
It is important to bear in mind that amplification within the audio band is not a particularly challenging application. Transistors are utilized not only within the context of audio amplification but also RF amplification, often at frequencies of several hundred gigahertz where linearity is equally as important.
With regard to your mention of square waves, this really has no bearing on the performance of an amplifier. The first thing to understand is that there is no such thing as a perfect square wave in reality. Illustrations such as the one below depict a purely mathematical concept, which is a square wave composed of an infinite series of sine waves. In order to produce or amplify a square wave such as the one below, you would require an infinite amount of bandwidth.
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When a square wave is passed through an amplifier or DAC, the resulting waveform can only be composed of sine waves representing the highest frequency that is possible within said amplifier's bandwidth. That is why the output sometimes exhibits a different appearance from that of the input when viewed on an oscilloscope, if the input contains harmonics beyond the amplifier's bandwidth. It has the effect of a low pass filter.
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Note that this has no bearing whatsoever upon the audible performance of the amplifier. A square wave composed of 20KHz sine waves already represents the highest frequency content that is audible to human beings and the vast majority of music is published at a sample rate of 44.1KHz.