Remember, a first order high pass filter will boost the bass before rolling it off. It's exactly like putting a woofer in a too small sealed enclosure. The f3 will be higher but the bass at the bottom of the passband will be boosted. This can tilt the tonal balance of the speaker more towards the bass, at the expense of low frequency extension. In fact, a whole lot of speakers are like that.
So, when your input low frequency pole is below about 2 Hz, then the effect at 20 Hz will be negligible. A 6 dB/octave low frequency pole with an f3 of 20 Hz will definitely intrude on the audible passband. It will boost the lowest notes in the passband (a bass hump), it will introduce time errors, and it will introduce distortion caused by any nonlinearities in the coupling capacitor. It is what's wrong with some commercial equipment, especially from the wayback machine.
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