An 8-bit audio signal has a theoretical maximum SNR of 48.16 dB
On the face of it, an 8-bit digitization process would increase "noise" by 3 dB (as per Brian Drummond's comment). However, when you take into account the natural "crest factor" for audio, the "noise" problem is worse: -
Image from here.
would an analogue audio (or video) signal with an SNR of <=48 dB only
be worth sampling at 8 bits?
The picture above is telling you that the main parts of the audio signal will be about 15 dB lower in RMS value compared to the peak value so, if you are listening to a piece of analogue music, the quieter areas will appear to have more noise. But, that regular noise might not be as annoying if you inserted an 8-bit ADC/DAC process in the signal chain. The added quantization noise will be more annoying and you may lose all audio information at very low signal levels.
So, if you listened to the audio from the 8-bit DAC output, it could be significantly worse (as a listening experience) than what you would expect if you analysed the degradation of signals based on peak/maximum levels.
The quieter areas would "appear" heavily distorted and noisy. The ADC/DAC system required to barely degrade the original signal would need to be significantly greater in bit depth than 8-bits, possibly more like 12 bits.
However, if the peak signal was quite loud and a volume control was used to lower the input signal by 20 dB (that's an approximate quartering of perceived loudness) then you would probably want to use a 16 bit ADC/DAC system.