Plenty of small omnis are extremely flat-response yet quite detailed, but the basic problem is the issue with a poor choir is variation of pitch, which any microphone will easily resolve. When we are discussing flatness of response, we are talking about maybe +/-3dB at various frequencies, but generally in the high frequency range. The fundamental pitches in error will be <500Hz. So while a microphone without a smooth response might not form an accurate stereo image, it can't make a bad choir sound good.
I agree - I don't think a microphone - even a pretty bad one - can hide mistakes like this at all. I'm a choir director, and no matter what mics I've used to record my groups, even built-in mics, all errors (especially pitch) are laid bare. It may not sound the best, but you can instantly hear any pitch, tone quality, vowel formation, or timing errors. This is a great teaching tool, as it reinforces to my students that I'm not completely crazy.
What using better equipment and technique has done to improve this for me as a teaching tool, is to make the imaging and presence far more true-to-life, and the resulting recording more pleasing to listen to. This makes my students more interested in listening to their performances to self-assess, even if it still painful to hear themselves. If your recording has good stereo imaging, you can also more clearly hear where individual errors are coming from. The painful self-analysis part is still true even on a relatively low-quality recording though.
A super-smooth treble is always going to sound better I guess, but for an a capella choir recording you likely won't notice such small inconsistencies. And if you do, it's probably only going to be a professional choir with flawless intonation in a great acoustic where you have a chance of those high harmonics being heard.