If the preamp outputs a positive voltage when the input signal is positive, the preamp does not invert phase (more properly called polarity). In this case the output signal is identical (except for amplitude) to the input signal.
If the preamp outputs a negative voltage when the input signal is positive (and also a positive voltage when the input is negative) then the preamp is said to invert phase (or invert polarity). In this case the output signal is a mirror image of the input signal.
If you're in the camp that believes that absolute polarity doesn't matter, then just relax and enjoy the music.
If you want the system to maintain absolute polarity, then you have to flip (i.e., invert or mirror image) the positive and negative going parts of the signal one more time.
The easiest way to accomplish this is to reverse the speaker connections as described above: right power amp + to right speaker -, right power amp - to right speaker +, etc.)
It has nothing to do with reversing channels.
BTW, the point of this exercise is to keep the speaker diaphrams in polarity with the original microphone polarity. In other words when the michrophone diagram moves inward in response to an air pressure wave we want the speaker diaphrams to move inwards as well.
Trouble is, recording studios don't normally keep track of polarity, and some studio gear inverts it. Thus some recordings are correct, and others have inverted polarity.
On multitracked recordings, the absolute polarity may even differ from track to track, so that the two channel mixdown cannot be polarity correct.
Some preamps and most digital processors provide a polarity (or phase invert) switch to allow you to cope with polarity problems on the fly.
So can you hear the effect of improper polarity? I think I can, but not on all recordings. Inverted polarity usually shows up as "woolly" bass and soundstage problems.
The effect of improper polarity is called the Wood effect after the guy who first documented it. These has been much written both pro and con on this topic.