It does correct each speaker separately. Now I'm not expert, but if you measure properly then you should get correction results as symmetric as your uncorrected response, so if you lack symmetry in the correction I suppose you also lacked symmetry without correction anyway, so imaging shouldn't be any worse than without correction?
The first-arrival sound is by far the most important for imaging, and imo sacrificing symmetry in the first-arrival sound in favor of symmetry in the in-room sound would not be conducive to good imaging.
Presumably the first-arrival sound from each of a stereo pair of loudspeakers is identical, up to the limits of production tolerances, but the in-room sound from each of a stereo pair of loudspeakers is virtually guaranteed to be different because rooms are virtually never acoustically symmetrical.
It is generally not possible to EQ a speaker's in-room response independent of the first-arrival sound. So to the extent that each speaker of a stereo pair is getting a different EQ in order to achieve the desired in-room response, the first-arrival sounds from the two speakers become increasingly dissimilar in frequency response.
At frequencies (in particular mid and high frequencies) where one speaker's first-arrival sound is louder than the other's, the image will be pulled towards the louder speaker.
I welcome correction from anyone who knows more about this than I do; I have zero experience with Audyssey.