I guess it all depends on what you mean by 'loss of bass timbre'. There will most likely be more power output in the range of the A-0 resonance, but it will certainly be at a higher pitch.
The A-0 mode is the lowest frequency one that can radiate sound effectively. Any lower resonance, like the 'neck mode', will be moving a surface so small relative to the wave length of the sound that it won't put out any appreciable amount of power. The air resonance pumps a lot of air, even though the hole is small relative to the wave lenght, so it gets by.
Any note you play that is below the 'main air' resonance will tend to lack power in the fundamental of the tone. This can make it sound 'nasal', and, although it might 'cut' well, the timbre can be a little 'thin' for many tastes.
Of course, the ability of the A-0 mode to support radiation of sound also decreases rapidly as you get above its pitch as well. The next resonance that can help out is the 'main top' mode, frequently about an octave higher. If the 'main air' or 'main top' mmodes have particularly narrow effective bands there can be quite a 'hole' in between, and in that case moving the 'main air' resonance up a little can help fill things in. This is usuallly not a probloem on flat top guitars, but might be on an archtop. most archtops have thier 'main air' resonance 4 to 6 semitones higher than the usual flatop. It's one of the big differences in the way they sound.
IMO it really doesn't pay to have the main air resonance end up as low as the fundamental of lowest note you're playing, and usually a second or third higher works out best. Much higher than a fourth above the lowest note also seems to be less desireable: I've measured some good Classical and Flat top guitars with the air resonances around A=110, but much higher than that seems the province of really cheap and tinny boxes. That's just my 'take'.
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